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High Resolution Coherent 2D Spectroscopy Peter C. Chen Chemistry Department, Spelman College, 350 Spelman Lane, Atlanta, Georgia 30314 ReceiVed: March 16, 2010; ReVised Manuscript ReceiVed: July 14, 2010
The purpose of this article is to describe recent progress on the use of coherent two-dimensional spectroscopy for investigating the electronic spectroscopy of gas phase molecules. Unlike conventional high resolution spectra where peaks are distributed along a single axis, high resolution coherent 2D spectra reveal informative patterns along two orthogonal frequency domains. The technique can successfully produce these patterns in situations where one-dimensional spectra appear patternless due to complexity and congestion. Molecular spectra that are difficult to analyze because of strongly perturbing effects (e.g., conical intersections) may be studied using this new technique. Several innovations, such as the ability to graphically separate rotational and vibrational information by clustering peaks and the ability to use multiple clusters to overcome spectral congestion help provide high resolution coherent 2D spectroscopy with the ability to analyze spectra that have previously resisted analysis. I. Introduction The well-established capabilities of multidimensional NMR have inspired a number of research groups to explore whether nonlinear (coherent) two-dimensional spectroscopy can provide comparable benefits in optical spectroscopy.1–7 Coherent spectroscopy is a natural choice for producing multidimensional spectra because it involves the generation of signals that depend upon the product of multiple fields that can be independently controlled in the time or frequency domain. For example, four wave mixing (FWM) can be used to produce spectra with up to four orthogonal dimensions through the manipulation of three input fields and one output field. Considerable effort has recently been focused on the development of new coherent 2D techniques that use ultrafast infrared pulses to extract new vibrational information from condensed phase samples.8–16 Progress has also been made in the development of new optical 2D techniques for studying electronic couplings and dynamics in condensed phase systems.17–19 A recent special issue of Accounts of Chemical Research includes 27 papers, most concerning the infrared region and all involving condensed phase samples.20 The focus of this paper, however, is on the use of high resolution coherent 2D spectroscopy as a new way to study complex electronic spectra of gas phase molecules.21,22 The electronic spectra of gas phase molecules are well-known for being incredibly rich and complex, often containing large numbers (thousands to millions) of peaks. Frequently, the density of states is so high that spectral congestion is a significant challenge. Over the years, spectroscopists have developed powerful tools and methods (e.g., high resolution lasers, supersonic jets, double resonance techniques) to help simplify, resolve, and interpret these spectra to study the detailed structure and behavior of molecules. While these tools and methods have worked remarkably well for simple small molecules, larger molecules yield spectra that are too congested and complex to analyze. Furthermore, even small molecules may exhibit unexpected behavior that remains challenging to interpret. For example, strong perturbations due to conical intersections can cause a breakdown of the Born-Oppenheimer approximation and the generation of unusually complex spectra. Once thought to be rare oddities, conical intersections are now
Peter C. Chen is a Professor of Chemistry at Spelman College. He received his A.B. from Cornell University in 1986 and his Ph.D. from the University of WisconsinsMadison in 1992. His graduate work was under the direction of Professor John C. Wright and involved the development of infrared four wave mixing techniques that helped lay the groundwork for the development of coherent multidimensional vibrational spectroscopy. His research interests include the development of new nonlinear multidimensional spectroscopic techniques and application to challenging systems that are important in atmospheric science.
believed to be ubiquitous in polyatomic molecules and responsible for many important effects (e.g., photosynthesis, vision, and charge transfer).23 The resulting spectra can appear very dense, congested, and perturbed. The following list includes some potential problems. 1. Very high peak densities caused by rotational and vibrational congestion may cause resolution and interpretation problems. The resulting spectra may appear as a broad patternless continuum under modest resolution conditions. The use and interpretation of more sophisticated techniques that provide higher resolution and/or selectivity may be difficult and time-consuming when information is gathered along a single dimension. 2. Samples containing larger molecules tend to have more isomers and isotopomers, resulting in greater spectral congestion. Traditional spectroscopic methods have difficulty distinguishing peaks that come from different species.
10.1021/jp102401s 2010 American Chemical Society Published on Web 09/23/2010
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3. Nonadiabiatic behavior due to conical intersections can increase the density of peaks, broaden the range over which peaks are observed, and perturb peak positions. Traditional methods can fail when used to predict and interpret such spectra. Spectral analysis relies heavily on pattern recognition, and the above problems make patterns difficult to identify. These difficulties have raised doubt about whether high resolution spectroscopy can be used to study larger molecules. A successful effort to extend the potential capabilities of high resolution spectroscopy to larger and more complicated molecular systems appears to require the development of more powerful techniques. One possible approach is to create new techniques that can produce multidimensional spectra. A high resolution form of coherent 2D spectroscopy has recently been developed to explore this idea. By distributing peaks over two orthogonal frequency dimensions, high resolution coherent two-dimensional (HRC2) spectroscopy provides new capabilities such as improved spectral resolution, multidimensional pattern recognition, and a number of new twodimensional concepts and innovations (e.g., information separation,peaksorting,andmulticlusteranalysis).Mostmultidimensional techniques (spectroscopy, chromatography, electrophoresis, etc.) provide a larger platform and a more convenient way to resolve and display large numbers of peaks. But coherent multidimensional techniques can provide important additional advantages as well. Examples in this paper illustrate how an appropriate choice of the two frequency dimensions and knowledge of how to interpret the resulting patterns can lead to solutions of specific problems such as those caused by severe spectral congestion and conical intersections. For example, perturbed and heavily congested regions of the NO2 spectrum (a prototype molecule for conical intersections) may be analyzed by setting one dimension to a difficult region and the other dimension to a region that is easier to analyze. Compared to incoherent spectroscopy, the use of coherent spectroscopy raises complications and provides advantages. First, several intense pulses of light must be overlapped and phase matched to generate an intense coherent output signal that is free of spectral interference from other incoherent processes. Second, the coherently generated signal can contain contributions from several different four wave mixing processes that may constructively or destructively interfere with each other. The existence of multiple FWM processes complicates matters because accurate analysis of the resulting spectra requires that these processes be identified, and this paper includes a brief discussion on how the observed 2D patterns can provide this needed information. The benefits of coherent spectroscopy include line narrowing (to remove effects from Doppler and inhomogeneous broadening) and the ability to achieve high spatial resolution that can be used for imaging and microscopy. Coherent spectroscopies do not rely on the creation of excited state populations; they work for nonfluorescing samples and do not require prior knowledge of excited state lifetimes and pathways. Certain coherent techniques are more restrictive than their incoherent counterparts; coherent techniques based on parametric FWM processes require that the final and initial states be identical. This paper describes how coherent spectroscopy can be used to produce high resolution multidimensional spectra of gas phase molecules in a way that facilitates the analysis of challenging systems. Like multidimensional NMR, coherent spectroscopy may be used to generate multiple resonances in the sample. These resonances may conveniently be achieved by using multiple
Chen
Figure 1. General format of a coherent 2D plot. Peaks along the diagonal (red and blue circles) are at the same location as those in conventional 1D spectroscopy. New information is displayed in the off-diagonal region; single resonances produce green horizontal and vertical single resonance lines that intersect to give two double resonance peaks (purple circles).
intense laser beams to produce a nonlinear optical signal from the sample. For isotropic samples, the third-order nonlinearity generates a FWM signal that involves three input fields and one output field.
| |[ ( )]
IFWM ≈ I1I2I3 χ(3) 2 sinc
L∆k 2
2
(1)
where the I’s correspond to the intensities of the three input fields, L is the wave-mixing path length, and sinc(L∆k/2) ) 1 when the fields are phase matched (∆k ) 0). The third-order nonlinearity χ(3) is a sum of contributing terms that are directly proportional to the product of four molecular transition dipole moments (µ), one associated with each field.
µiµjµkµl i,j,k ∆i∆j∆k
χ(3) ≈ ∑
(2)
where the µ’s are transition dipole moments for the four interactions. The three resonance denominators have the general expression ∆ ) δ - iΓ, where δ is the difference between molecular transition frequencies and laser frequencies and Γ is the dephasing rate. Spectra can be produced by monitoring the intensity of the output beam as a function of the field frequencies. If none of the field frequencies are resonant, the resonances’ denominators are large and real, and only broad featureless nonresonant signals are observed. Resonance enhancement is achieved when one or more field frequencies match appropriate differences between energy levels in the molecule. At resonance, δ ) 0, ∆ collapses to -iΓ, and the amplitude of the nonlinear oscillation increases, producing a resonance peak in the spectrum. The maximum resonance enhancement is achieved when all three resonance denominators collapse, a situation referred to as triply resonant or fully resonant FWM. Single resonance enhancements are sufficient for producing peaks in (conventional) 1D coherent spectra, but multiple resonances are needed to generate a peak in coherent 2D spectroscopy. Therefore, the underlying foundation for coherent 2D spectroscopy is multiresonant nonlinear spectroscopy.24 Figure 1 shows the contour structure of a model coherent 2D spectrum where the intensity (out of page) is a function of two field frequencies (ωn and ωm). The information along the diagonal is similar to that found in conventional 1D spectra, and new information is located in the off-diagonal region.6 A
Feature Article single resonance that produces a peak in a coherent 1D spectrum may produce a resonance line in a coherent 2D spectrum. These singly resonant lines may be horizontal, vertical, or diagonal in direction.25 For example, a resonance denominator like ∆ ) ωtransition - ωm - iΓ or ∆ ) ωtransition - ωn - iΓ will produce a vertical or horizontal resonance line. On the other hand, a resonance denominator like ∆ ) ωtransition - (ωm - ωn) - iΓ produces a diagonal resonance line with a slope equal to 1 and a y-intercept equal to -ωtransition. Singly resonant lines may intersect, and when they do, they may produce a doubly resonant enhancement (two resonance denominators become complex) if both resonances come from the same FWM process and the same molecule. The resulting doubly resonant peaks may be orders of magnitude stronger than the singly resonant features. When the sample is a freely rotating gas phase molecule, the number of singly resonant lines that may be formed in HRC2 spectroscopy can be very large due to the high density of rotational levels. At first, it might appear that the number of intersections and double resonance peaks would be overwhelming. However, FWM processes may constrain the number of observed double resonance peaks, making the resulting 2D patterns easier to identify and analyze than their counterparts in 1D spectroscopy. Furthermore, the number and type of participating states is often more tightly controlled in coherent spectroscopy compared to incoherent techniques. Subsequently, spectra that otherwise appear impossible to unravel may be conveniently analyzed using coherent 2D spectroscopy. The remainder of this paper will describe the production of coherent 2D spectra, the interpretation of such spectra, and introduction of powerful new analysis tools for dealing with “difficult” molecules. II. Experimental Methods Coherent 2D spectra may be produced using time-domain, frequency-domain, or mixed time-and-frequency-domain approaches.2,26,27 For condensed phase experiments, time-domain Fourier transform experiments that use short pulsed lasers offer important advantages such as temporal rejection of the shortlived nonresonant background that might otherwise obscure weak peaks. High repetition rate, short pulsed lasers are also useful for studying photolabile samples while minimizing sample damage, and the ability to study processes with subpicosecond time resolution is especially useful for studying fast processes. Although highly effective for generating coherent 2D spectra in the infrared region, this approach is not so attractive for producing high resolution spectra in the visible and/or UV region because the requirements for long-term phase stability are difficult to achieve.28 On the other hand, a frequency-domain approach that uses a combination of narrowband and broad-band lasers with multichannel detection is attractive because it produces high resolution spectra quickly, it provides a wide dynamic range, and noise is reduced due to multichannel acquisition. Spectral acquisition rates are an important consideration because producing 2D spectra requires more data and therefore consumes more time than producing 1D spectra. Fortunately, recent improvements in lasers, multichannel detectors, optics, and computers facilitate expansion into the second dimension. Figure 2 shows a simplified layout for the experimental system. A narrow-band tunable visible/UV beam from a Spectraphysics MOPO-730 or Coherent Scanmate Pro dye laser generates resonances between levels of the ground and excited electronic states of the sample molecule. This beam is overlapped with a broad-band near-infrared beam (continuous
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Figure 2. Simplified layout of the experimental setup.
emission from 1050-1700 nm) that is created using a homebuilt degenerate optical parametric oscillator that is pumped at 683 nm by a Nd:YAG laser-pumped hydrogen Raman cell. Two near-infrared photons of different frequencies from this broadband source provide two input fields in the resulting dual-broadband FWM process. The use of near-infrared light limits the number of electronic resonance enhancements since relatively few molecules have electronic levels in the 1050-1700 nm region. The spatially overlapped broad-band and tunable narrow-band beams are focused in the sample to produce the coherent output beam. This output beam is separated from the input beams using absorptive glass filters (KG-3 and BG-40) and notch filters. Alternatively, BOXCARS phase-matching may be used instead of collinear phase matching. In either case, the coherent output beam is focused into a 1.25 m Czerny-Turner monochromator (SPEX 1250 m) equipped with an array detector (e.g., 2048 × 512 pixel CCD) that permits rapid multichannel detection. The narrow-band laser is then tuned while the generated spectra are stacked. The resulting coherent 2D spectrum shows the intensity of the FWM signal (along the z-axis) as a function of the tunable narrow-band laser wavelength λn along the y-axis and the monochromator detection wavelength λm along the x-axis. The spectral resolution of the instrument along the y-axis depends upon the linewidth of the narrow-band tunable laser and the resolution along the x-axis depends upon the monochromator/CCD system. The pulse energies are typically 1-3 mJ for the narrow-band visible beam and 5-10 mJ for the broad-band near-infrared beam. The narrow-band tunable laser beam wavelength is advanced at a rate of approximately 1 step/s (10 shots), and the time required to produce coherent 2D spectra ranges from 104 peaks), so reducing a 2D spectrum to a 2D plot is often needed to analyze such spectra. III. Results and Discussion Figure 3 shows a conventional 1D absorption spectrum (top) and a coherent 2D spectrum (bottom, with peaks that come out of the page and appear as dots) of iodine vapor. A conventional energy level diagram is also shown for the absorption process and a wave-mixing energy level (WMEL) diagram is shown for the FWM process responsible for producing the 2D spectrum. Each arrow in a WMEL diagram represents a coherence (a field-induced change in either the bra or the ket) rather than a change in population (resulting in a change in both the bra and ket). The wavelengths λm and λn on the x and y axes correspond to the frequencies ωm and ωn on the WMEL diagram, so the intensities of the peaks in the 2D spectrum
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Figure 3. Conventional 1D absorption spectrum (top) and coherent 2D spectrum (bottom) of iodine. In the 1D spectrum, peaks from different kinds of transitions (e.g., those starting at v′′ ) 0 and those starting at v′′ ) 1) overlap. In the coherent 2D spectrum, the v′′ ) 1 peaks are clustered into parabolas that appear slightly shifted (up and to the right) of the parabolas that contain the v′ ) 0 peaks. The centers of the clusters for the v′′ ) 0 peaks are circled in red and those for the v′′ ) 1 peaks (that also appear weaker on the left side of the 1D spectrum) are circled in green. For the wave-mixing energy level diagram, solid horizontal lines represent real levels and a broken horizontal line indicates a virtual level.
depend upon dual electronic resonances that both involve the same ground state rovibrational level. For the 1D absorption spectrum, each transition is independent and all peaks appear along a single axis. Displaying spectral information along a single axis causes several common problems: (1) rotational congestion between peaks that have similar ∆v ) v′ - v′′ values, (2) vibrational congestion between the v′′ ) 0 peaks and the v′′ ) 1 peaks, and (3) insufficient spectral resolution. The improved clarity of the 2D spectrum illustrates the effective use of a second dimension allows HRC2 spectroscopy to survey a larger numbers of peaks with improved spectral resolution. The FWM process shown in Figure 3 is referred to as coherent double resonance electronic spectroscopy (CDRES). Other FWM processes may be possible, but the CDRES process appears to be favored by the experimental system. Furthermore, the high level of symmetry produced by CDRES provides a level of simplicity that is beneficial when dealing with complex spectra. For example, both of the fields ωn and ωm connect the ground state to an excited electronic state, so the technique primarily probes vibrational levels in the excited electronic state (i.e., vibronic levels). Other FWM processes (e.g., the more widely known technique of resonantly enhanced coherent antiStokes Raman spectroscopy, or RECARS) involve resonances between many vibrational levels of the ground electronic state and many vibrational levels of the excited electronic state. Therefore, processes like RECARS may provide more information (e.g., both ground state vibrational and excited state vibration levels are probed), but the resulting spectra are more complicated and more difficult to interpret. The CDRES spectrum in Figure 3 shows two kinds of regular repeating patterns. First, the peaks appear to be grouped into parabola-shaped clusters. Second, the clusters themselves appear to be arranged in a regular repeating pattern (denoted by the red and green circles). These two kinds of patterns are observed because use of the second dimension facilitates the spatial separation of rovibrational peaks by their vibrational resonances.
Chen Whenever the vibrational energies are greater than rotational energies, the peaks in the CDRES spectrum will form these two types of patterns: (1) a narrow rotation-dependent pattern, and (2) a wider vibration-dependent pattern. First, peaks produced by the same vibrational resonances are grouped into individual clusters that bear some resemblance to Fortrat parabola.30 This clustering occurs because the spacing between rotational energies and the relatively selective and robust rotational selection rules (e.g., ∆J ) (1) cause the distance between consecutive rotational peaks to be small and relatively consistent. All rotational peaks within a given cluster will involve the same dual vibronic resonances (vx′′ f vx′ and vy′′f vy′, where vx′′ and vx′ represent the lower and upper vibrational quantum numbers along the ωm axis and vy′′ and vy′ are vibrational quantum numbers along the ωn axis). Within each cluster, the rotational peaks form multiple branches (similar to those in a Fortrat parabola) in which the peaks are ordered sequentially by rotational quantum number (J). Therefore, the formation of clusters facilitates peak assignment because all the peaks within a cluster have the same vibrational quantum numbers (vx′, vy′, vx′′, and vx′′) and sequential arrangement of peaks by J′′ within each branch permits identification of the rotational quantum numbers. Second, these clusters are aligned vertically and horizontally so that they form grids composed of repeating rows and columns. CDRES is a parametric FWM process (initial state ) final state), so vx′′ ) vy′′. One consequence is that the set of all possible vibronic levels probed by the first photon ωn is the same as the set of all possible vibronic levels spanned by the last photon ωm. The locations of the clusters therefore depend solely upon the energies of the vibronic levels and only the lowest initially populated ground state vibrational level(s). Analysis of this second pattern subsequently leads directly to the location of the vibronic levels and their corresponding vibrational quantum numbers, which are ordered sequentially within a grid. The use of two orthogonal dimensions to spatially separate vibrational and rotation information into different types of patterns that appear ordered sequentially by vibrational and rotational quantum numbers helps simplify analysis of the spectra. CDRES also provides a means for spatially separating hot bands from cold bands. Below 550 nm, the room temperature iodine absorption spectrum is dominated by cold bands (due to transitions from v′′ ) 0) and above 564 nm, it is dominated by hot bands (due to transitions from V > 0). The region between 550 and 564 nm contains overlapping peaks from both cold and hot bands. In Figure 3, the centers of the clusters produced by molecules that originally start at v′′ ) 0 are circled in red. The hot parabolas (from molecules initially at v′′ ) 1) form a separate grid of clusters (shown by the green circles) that grow in intensity with increasing wavelength along the x-axis. Therefore, HRC2 spectroscopy can help resolve vibrational congestion as well as rotational congestion. The first type of pattern, the internal shape within a cluster, reveals the relationship between the excited state and ground state rotational constants in a way that is simple and immediately recognizable. The left side of Figure 4 shows the predicted shape of a single cluster produced by CDRES if all rotational constants are identical (e.g., B′ ) B′′) for all levels and the rotational selection rule is ∆J ) (1. The cluster is formed by concentric boxes that are numbered sequentially by the ground state rotational constant J′′. Figure 5 helps illustrate how the boxes that comprise the X-shaped cluster are formed. Along each axis is a simulated 1D absorption spectrum showing a group of resolved rotational peaks from a single vibronic transition. Each
Feature Article
Figure 4. Left: predicted shape of a cluster produced by CDRES, assuming B′ d B′′ for both axes and a rotational selection rule of ∆J ) (1. Only a few J′′ values are shown here; higher values follow the same pattern. Four peaks with identical J′′ values form a box. Near the center, the gray point is the solitary J′′ ) 0 peak and the X marks the location of the vibronic origin. Right: similar features for a cluster that is parabolic because B′ * B′′ for both axes (B′ > B′′ along the y-axis and B′ < B′′ along the x-axis).
Figure 5. Relationship between rotational peaks in conventional 1D spectra (left and bottom), their corresponding vertical and horizontal resonance lines in a 2D spectrum, and their points of intersection. These intersection points that produce CDRES peaks are represented by the black dots and occur only for intersecting resonance lines that have identical J′′ values.
field frequency that can produce an absorption transition can also produce one or more singly resonant lines in a coherent 2D spectrum. The energy levels responsible for the rotationally resolved peaks along the y-axis absorption spectrum can also generate horizontal resonance lines in the coherent 2D spectrum, and levels responsible for producing rotational peaks along the x-axis absorption spectrum also produce vertical resonance lines in the coherent 2D spectrum. As discussed earlier, two singly resonant lines can intersect to form a more intense doubly resonant peak if two resonances occur on the same molecule and through the same process. CDRES is a parametric process where the initial state and final state must be identical. Therefore, most of the points of intersection will not produce a doubly resonant peak because the value of the ground state rotational quantum number J′′ for the x-axis (ωm) is not the same as the J′′ value for the y-axis (ωn). The points of intersection from lines that have equal J′′ values form the corners of a box. For a simple rigid rotor, the dimension of a box equals 4B′(J′′ + 1 /2) along each axis. The J′′ )0 peak is a solitary peak found near the center of the cluster but is shifted in both the x and y direction by B′ from the exact center of the X and is shifted by 2B′ from the rotationless vibronic origin. The smallest box is made of four peaks with J′′ ) 1 and J′ ) 0 or 2 for both axes. Larger values of J′′ produce larger boxes, and the four corners
J. Phys. Chem. A, Vol. 114, No. 43, 2010 11369 of the boxes can be viewed as four branches that can be labeled PP, PR, RP, or RR. A perfect X-shaped cluster results only if the rotational constants in the lower state and both upper states are identical. If the rotational constant B′ in either upper electronic state differs (by more than approximately 10%) from the rotational constant B′′ in the lower (ground) electronic state, then boxes will no longer remain concentric. Instead, the centers of the boxes will shift, causing the X-shaped cluster to appear distorted and parabolic (see the right side of Figure 4). For a simple rigid rotor, the center of each box for each axis is located at a distance of ∆BJ′′2 + ∆BJ′′ +B′ from the vibronic origin (∆B ) B′ B′′ for the rotational constants along that axis). Therefore, the shift grows at a rate of 2∆B per J′′. A similar effect is observed with Fortrat parabolas, which are either degraded to the red when B′ < B′′ or degraded to the blue when B′ > B′′. For the iodine spectra in Figure 3, B′ < B′′ for both axes, so the clusters appear as parabolas that are degraded toward the red. The clusters produced by HRC2 spectroscopy may be described as double Fortrat parabolas. The Fortrat plot is a well-known analysis tool for visualizing the rotational structure of a vibrational or vibronic band that requires an accurate determination of the rotational quantum numbers. In CDRES spectra, these parabolas are generated automatically by the experiment in a way that reVeals the rotational quantum numbers. Furthermore, they contain separate x-axis and y-axis peak spacings that depend upon separate ωm and ωn resonances and separate sets of spectroscopic constants. These two resonances can involve the same electronic levels, but they may also involve different excited electronic states, allowing one to observe effects from two different excited electronic states. Therefore, these parabolas may be considered as an experimental fusion of two Fortrat parabolas that are selectively connected through a common ground level (i.e., only points with the same J′′ value are merged). When the two axes in a CDRES spectrum correspond to ωn and ωm, the resulting parabolas are distributed in a grid of rows and columns that are ordered by vibronic quantum number because the energies of the vibronic levels of a harmonic oscillator increase systematically with vibronic quantum number. If the sample consists of identical diatomic molecules at a relatively low temperature, a single grid may be observed, and the pattern may be relatively simple. At higher temperatures, hot bands can produce additional grids, as discussed earlier and shown for iodine in Figure 3. If the sample contains isotopomers or molecules that have multiple vibrational degrees of freedom, multiple grids may also be observed. The existence of multiple grids can complicate the 2D spectra, but the regular spacing between rows and columns of a single grid (the spacing may not be exactly equal due to vibrational anharmonicity) created by the CDRES process helps make the patterns identifiable and discernible. For example, Figure 6 shows simulated and experimental HRC2 spectra containing multiple grids caused by the three isotopomers of Br2. The existence of isotopomers usually causes considerable difficulty when trying to interpret a conventional 1D spectrum. In the HRC2 spectrum, the Br2 peaks are still organized into recognizable clusters, which are then organized into rows and columns of clusters according to vibronic quantum number. Since each isotopomer has a slightly different vibronic frequency,31,32 the rows and columns of clusters for the different isotopomers are located at slightly different positions. Therefore, CDRES spectroscopy can also organize peaks into separate clusters and grids according to isotopomeric species.
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Figure 6. Simulated (top) and experimental (bottom) high resolution coherent 2D spectra of Br2 showing a pattern of rows and columns. The high level of organization in such CDRES spectra makes it convenient to determine the isotopomer, vibrational quantum numbers, and rotational quantum numbers for any peak.
Figure 7. Wave-mixing energy level diagrams and simulated clusters for CDRES and RECARS. The CDRES peaks and clusters align both vertically and horizontally. For RECARS, the peaks and clusters align vertically but not horizontally.
One concern with multiresonant coherent spectroscopy is the possibility of contributions from FWM processes other than the one intended. For example, while CDRES has been observed to be the dominant process in the acquired HRC2 spectra of I2 and Br2, peaks from RECARS (wave-mixing energy level diagram shown in Figure 7) have been observed in the HRC2 spectra of C2.33 If multiple FWM processes contribute peaks, then it will be necessary to identify them to accurately interpret and analyze the resulting coherent 2D spectra. Fortunately, the pattern formed by clusters produced by RECARS is different from the pattern formed by CDRES clusters. The clusters produced by CDRES form a rectangular grid, consisting of horizontal rows and vertical columns. In other words, the clusters align vertically and horizontally. On the other hand, clusters produced by RECARS form a parallelogram grid; the clusters align vertically but not horizontally (see Figure 7). To this date, CARS, RECARS, and CDRES are the only FWM processes that have been identified in HRC2 spectra. Other potential FWM processes are expected to be relatively weak because they require that the molecule have strong transition dipoles in the near-infrared region, which is relatively rare.
Chen HRC2 spectroscopy can also be useful for systems where severe perturbations cause spectra to deviate from traditional models. NO2 has long served as a prototype model for studying conical intersections; it has an electronic spectrum that is notorious for resisting conventional methods of analysis. The NO2 molecule is also an important atmospheric pollutant and is one of the few triatomic molecules that absorbs light throughout the visible region. Analysis of the visible NO2 spectrum is needed because of the important photochemistry involving sunlight in urban areas where the concentration of NO2 is high.34–36 The molecule behaves like a prolate nearsymmetric rotor with a ground state rotational constant B′′ ) (B′′ + C′′)/2 ) 0.422 cm-1.37 It also has an odd number of electrons, so the total angular momentum depends on the interaction between the electron spin (S ) 1/2) and the rotational angular momentum (N). This interaction splits each N level into two components, and the size of the splitting depends upon the value of N and the spin-rotation constant ε ) (εbb + εcc)/2. The value of this constant in the ground state (∼10-3 cm-1) is small, but the values in the excited state may be more than 1 order of magnitude larger, causing fine splittings that are relatively easy to resolve. The visible spectrum of NO2 was first described by Brewster in 1834, first sketched by Miller in 1845, and first photographed in 1928 by Carwile.38 Over time, an impressive number of researchers have applied a vast array of techniques to study the visible spectrum of NO2, making it one of the longest and most heavily studied molecules in history. For example, two wellknown atlases38,39 have been published, each containing more than 10 000 unassigned peaks distributed over 100 pages of spectra. These atlases cover only a fraction of the visible region for a molecule that absorbs continuously from the infrared to the UV region. In 1975, Smalley and co-workers applied molecular jet spectroscopy to NO2 to help simplify this enormously complex spectrum.40 The results indicated a density of vibronic origins that was 1 order of magnitude greater than expected and that had irregular spacings. That same year, Gillespie and co-workers published the results of their calculational studies that were in agreement with experimental results.41 Even if their high resolution spectra appear rotationally congested, well-behaved triatomic molecules usually have a low resolution room temperature electronic absorption spectrum with a regular and easily recognizable structure that can be attributed to the vibronic levels. In contrast, the visible spectrum of NO2 (see Figure 8) is unusually broad and is largely void of regular patterns. Under high resolution, the only near-visible regions that exhibit regular structure are in the UV region from 370 to 460 nm42 and the near-infrared region below 12 000 cm-1.43 Throughout the visible region, the spectrum shows severe congestion and is not assignable due to the unusually high density of vibronic bands that have irregular rotational structures.44 This observation is attributed to the existence of multiple conical intersections, the first starting at a low energy of approximately 10 000 cm-1 between the ground state X2A1 and the first excited electronic state A2B2. The asymmetric vibrations (b2) of the X2A1 state have the appropriate symmetry to interact with the a1 vibrations of the A2B2 state. The resulting hybrid vibronic states are mixtures of highly excited vibrational levels of the ground electronic state and the vibrational levels of the first electronic level.44 The density of these mixed vibronic levels is unusually high (average spacing 105 peaks). Use of a filter based on previously assigned resonances reduces the number of peaks by 2 orders of magnitude and helps uncover X-shaped patterns, not shown (the resulting peak positions shown without intensity information are shown on the bottom 2D plot). The y-axis range (592.6-594.1 nm) for the bottom plot is the same as that for the top plot. The red points on the bottom plot indicate the predicted cluster centers based on literature values for the vibronic origins.
(in this case, the Ka ) 0 peaks of the 593.3 nm cluster21). After filtering, the number of peaks dropped by almost 2 orders of magnitude and the resulting plot provides a clearer picture of the X-shaped clusters (see the lower 2D plot in Figure 11). These results suggest that the following general approach to analyzing HRC2 spectra might be effective: first use previously assigned resonances (e.g., from the literature) to assign peaks in clusters that are clear and easy to analyze, and then use these points to help “filter” and analyze more difficult and congested clusters that have the same horizontal or vertical resonances. This approach may be continued until the entire region of interest has been successfully analyzed. One possible concern is the accuracy of the resulting assignments; how does one know whether the results are correct? The level of confidence can be raised by comparing results from two or more separate methods of analysis. One traditional method is to determine the fit between the observed wavelength of assigned peak and the corresponding values predicted by models (e.g., nonrigid rotor and anharmonic oscillator models). In HRC2 spectroscopy, peaks that have been assigned can be checked using this approach along both axes. This kind of approach usually works best if the peaks are not severely perturbed. Another method that employs an experimental approach is to use spectral selectivity offered by certain forms of spectroscopy. The successful assignment of peaks in the 593.3 nm region (refs 52–54) relied on the selectivity of spectroscopic techniques such as dispersed laser induced fluorescence, where only certain transitions are allowed. The peaks produced in HRC2 spectra rely on resonance enhancements that employs similar (but not identical) selectivity. However, CDRES provides many additional advantages, including higher spectral resolution, the ability to handle a much larger number of peaks, and the ability to compare assignments made by multiple clusters that fall upon the same column or row and therefore have the same x-axis or y-axis resonances. For relatively simple spectra such as those produced by iodine and bromine, these two approaches are probably sufficient to provide a satisfactory level of confidence in the results. For extremely challenging samples such as NO2, however, the availability of additional approaches may be useful to further ensure accuracy and elevate confidence in the results. For example, a reliable, independent approach based solely on the detailed structure of the clusters (not based on prior assignments) could be useful as a third method for determining or verifying assignments. Development of suitable pattern-recognition algorithms should be possible, given the specific relationship between the detailed structure of the clusters and the spectroscopic constants, selection rules, and quantum num-
bers. Such a method would also be useful when spectra of molecules that have no prior excited state rotational assignments are analyzed. In the future, the relationship between HRC2 spectroscopy and molecular jet spectroscopy may prove to be an interesting one. The ability to identify vibronic origins, marked near the centers of the clusters, suggests that CDRES may provide either identical or complementary information to that of molecular beams spectroscopy. Furthermore, HRC2 retains all rotational information, so this approach can be used to assign room temperature NO2 peaks throughout the visible region. The process outlined above is relatively efficient (peaks from numerous vibronic origins are currently being assigned) and my research group intends to publish assignments for a large set of vibronic origins in the near future. During these studies, the location of vibronic origins identified by molecular jet spectroscopy is being used to predict and confirm the location of clusters. Jost and co-workers used molecular jet spectroscopy to produce a high quality list of vibronic origins for NO2 that covers 11 200-16 150 cm-1 63 and 16 000-19 360 cm-1.64 This list was used to mark spots (red dots) in Figure 11 where the centers of X-shaped clusters should be located. They were also used to add markers indicating the expected location of cluster columns and rows along the x-axis and y-axis of Figure 9. IV. Conclusions Spectral congestion and complexity have limited the ability to use high resolution electronic gas phase spectroscopy to study large molecules and small molecules that are complicated by nonadiabatic behavior. HRC2 spectroscopy appears to be an effective survey technique for dealing with the notoriously complex spectrum of NO2; it provides a two-dimensional platform for organizing peaks into useful patterns. The resulting graphical approach facilitates the assignment of peaks, even if the positions have been perturbed and the spacings between peaks are irregular. Irregular behavior can be easily identified, extra peaks can be neglected, and multicluster analysis methods may be used to help assign peaks correctly. In general, the following features make HRC2 spectroscopy attractive for dealing with spectra that might otherwise be too difficult to analyze. 1. Improved resolution and information processing a. Effective use of the second dimension provides higher resolution and improved pattern recognition. b. Rotational information can be spatially separated from vibrational information. c. Peaks are separated by selection rule and isotopomer. d. Large numbers of peaks (e.g., thousands to millions) may be simultaneously separated, sorted, and assigned.
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e. The identity of the optical process responsible for generating a group of peaks may be quickly and easily determined. 2. Alternative method for analyzing perturbed spectra a. Spectroscopic constants may be estimated by simply observing the shapes of generated clusters. b. Regions may be broadly surveyed to determine which clusters are easiest to analyze. c. Rotational peaks for a given vibronic origin may be assigned rapidly by using graphical methods, even if the peak positions are perturbed and peak spacings are irregular. 2. Multicluster capabilities a. An assigned cluster may be used to help analyze other clusters, including those in heavily congested regions. b. Multiple clusters may be compared to confirm assignments and improve accuracy. Further development of HRC2 spectroscopy might lead to capabilities and methods that are of broad interest. For example, could two-dimensional spectroscopy be used to directly detect and confirm the presence of conical intersections? The ability to display large amounts of vibrational and rotational information in a highly organized way opens the possibility that conical intersections may leave readily identifiable signatures in the HRC2 spectra. What are the limitations of HRC2 spectroscopy, and could coherent 3D or 4D spectroscopy further extend these limits and provide additional selectivity? The ability to resolve and easily analyze peaks using the approaches described in this paper will undoubtedly be tested when applied to larger and more complex molecular systems. Additional selectivity provided by adding higher dimensions might further extend our ability to use spectroscopy to study the structure and behavior of molecules. Finally, what kinds of new analysis tools might be developed to further expand the capabilities of high resolution coherent multidimensional spectroscopy? New twodimensional analysis tools based solely upon pattern recognition of cluster shape and structure might be useful for verifying assignments and for helping accelerate the analysis of large and complex spectra. Further development and application of this new technique may help solve some longstanding problems in spectroscopy and may expand the capabilities of high resolution spectroscopy to larger and more complicated molecular systems. Acknowledgment. I thank all present and past group members, especially Candace C. Joyner and Kamilah Mitchell. I am grateful to John Wright, Michael Heaven, and Beatriz Cardelino for their helpful comments and discussions. I also thank Frank Delaglio for developing the 2D peak picking software. This work was supported by the National Science Foundation under grants CHE-0616661, EEC0310717, and CHE-0910232. References and Notes (1) Zhao, W.; Wright, J. C. Phys. ReV. Lett. 2000, 84, 1411–1414. (2) Pakoulev, A. V.; Rickard, M. A.; Meyers, K. A.; Kornau, K.; Mathew, N. A.; Thompson, D. C.; Wright, J. C. J. Phys. Chem. A 2006, 110, 3352–3355. (3) Tian, P.; Keusters, D.; Suzaki, Y.; Warren, W. S. Science 2003, 300, 1553–1555. (4) Scheurer, C.; Mukamel, S. J. Chem. Phys. 2002, 116, 6803–6816. (5) Zanni, M. T.; Hochstrasser, R. M. Curr. Opin. Struct. Biol. 2001, 11, 516–522. (6) Jonas, D. M. Annu. ReV. Phys. Chem. 2003, 54, 425–463.
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