Peak Separation and Sorting by Coherent 2D Resonance Raman Spectroscopy

Multidimensional Pattern Recognition in High-Resolution 2D and 3D Spectra of Gas-Phase Molecules

ConspectusWhen molecules transition from the condensed phase to the gas phase, their spectra undergo a dramatic transformation as well; each peak in a condensed-phase spectrum can yield thousands of peaks in the gas phase because the molecules are free to rotate and those rotational motions are quantized. These gas-phase spectra contain a wealth of detailed information about molecular structure and behavior, but peak densities are often so high that congestion obscures the patterns needed to assign peaks and extract molecular constants. This Account describes how coherent multidimensional techniques not only reduce peak densities and congestion in gas-phase spectra but also create multidimensional patterns that are easy to recognize and interpret. First, all peaks with the same vibrational quantum numbers form rotational patterns such as X's, double parabolas, and asterisks. These rotational patterns are composed of basic units and can provide immediate information about the molecule's structure, behavior, and rotational selection rules. Second, groups of these rotational patterns can be arranged into vibrational patterns that form arrays of rectangles or parallelograms. These vibrational patterns can be used to determine wave-mixing processes and measure vibrational constants. Coherent multidimensional spectroscopy therefore automatically separates vibrational and rotational information and then sorts peaks by vibrational and rotational quantum number. Furthermore, if the sample is composed of a mixture, then these patterns can also sort peaks by species, and higher-dimensional techniques can even provide the ability to select a species in the mixture. These techniques have successfully produced highly patterned 2D and 3D spectra for samples that otherwise generate patternless spectra such as isotopologue mixtures and vibronically perturbed molecules such as NO₂.High densities of states can lead to congestion and perturbations that make it difficult to accurately assign peaks using the information that is traditionally available from 1D spectra: a peak's intensity and its frequency. Coherent 2D and 3D techniques are well-suited for dealing with and learning from perturbations because the coordinate of each peak in multidimensional space includes multiple frequency values. Accurate assignments are possible when peaks in 2D or 3D spectra that are perturbed along one frequency axis are unperturbed along an orthogonal frequency axis. Furthermore, patterns often repeat in adjacent rows or columns, so regions that are less congested can be used to resolve or identify key peaks or patterns in regions that are severely congested. Perturbations can make the spacings within multidimensional rotational and vibrational patterns slightly irregular, but these automatically generated patterns remain easy to recognize and analyze.This Account describes three high-resolution coherent multidimensional spectroscopy techniques, the types of patterns they can produce, and how information can be extracted from these patterns. This work is being conducted at Spelman College, a historically Black college for women where all of the students are undergraduates. The resulting techniques are not only highly effective for dealing with some of the most congested, perturbed, and challenging spectroscopic systems, but they are relatively easy to use, moderate in price to set up, and quick to run.

Two-dimensional pattern recognition methods for rapidly recording and interpreting high resolution coherent three-dimensional spectra

High resolution coherent multidimensional spectroscopy has the ability to reduce congestion and automatically sort peaks by species and quantum numbers, even for simple mixtures and molecules that are extensively perturbed. The two-dimensional version is relatively simple to carry out, and the results are easy to interpret, but its ability to deal with severe spectral congestion is limited. Three-dimensional spectroscopy is considerably more complicated and time-consuming than two-dimensional spectroscopy, but it provides the spectral resolution needed for more challenging systems. This paper describes how to design high resolution coherent 3D spectroscopy experiments so that a small number of strategically positioned 2D scans may be used instead of recording all the data required for a 3D plot. This faster and simpler approach uses new pattern recognition methods to interpret the results. Key factors that affect the resulting patterns include the scanning strategy and the four wave mixing process. Optimum four wave mixing (FWM) processes and scanning strategies have been identified, and methods for identifying the FWM process from the observed patterns have been developed. Experiments based on nonparametric FWM processes provide significant pattern recognition and efficiency advantages over those based on parametric processes. Alternative scanning strategies that use synchronous scanning and asynchronous scanning to create new kinds of patterns have also been identified. Rotating the resulting patterns in 3D space leads to an insight into similarities in the patterns produced by different FWM processes.

An Introduction to Coherent Multidimensional Spectroscopy

Coherent multidimensional spectroscopy is a field that has drawn much attention as an optical analogue to multidimensional nuclear magnetic resonance imaging. Coherent multidimensional spectroscopic techniques produce spectra that show the magnitude of an optical signal as a function of two or more pulsed laser frequencies. Spectra can be collected in either the frequency or the time domain. In addition to improving resolution and overcoming spectral congestion, coherent multidimensional spectroscopy provides the ability to investigate and conduct studies based upon the relationship between different peaks. The purpose of this paper is to provide a general introduction to the area of coherent multidimensional spectroscopy, to provide a brief overview of current experimental approaches, and to discuss some emerging developments in this relatively young field.

High resolution coherent three dimensional spectroscopy of NO2

Expansion from coherent 2D spectroscopy to coherent 3D spectroscopy can provide significant advantages when studying molecules that have heavily perturbed energy levels. This paper illustrates such advantages by demonstrating how high resolution coherent 3D (HRC3D) spectroscopy can be used to study a portion of the visible spectrum of nitrogen dioxide. High resolution coherent 2D spectra usually contain rotational and vibrational patterns that are easy to analyze, but severe congestion and complexity preclude its effective use for many parts of the NO2 spectrum. HRC3D spectroscopy appears to be much more effective; multidimensional rotational and vibrational patterns produced by this new technique are easy to identify even in the presence of strong perturbations. A method for assigning peaks, which is based upon analyzing the resulting multidimensional patterns, has been developed. The higher level of multidimensionality is useful for reducing uncertainty in peak assignments, improving spectral resolution, providing simultaneous information on multiple levels and states, and predicting, verifying, and categorizing peaks.

Rotational and vibrational pattern interpretation for high-resolution coherent 3D spectroscopy

High-resolution coherent multidimensional spectroscopy provides an alternative to conventional methods for generating rotationally resolved electronic spectra of gas phase molecules. In addition to revealing information such as the relationships among peaks, it can provide clearly recognizable patterns for spectra that otherwise appear patternless due to rotational congestion. Despite this improvement, high-resolution coherent 2D spectroscopy can still exhibit congestion problems; expansion to the second dimension is often not sufficient to prevent overlapping of peaks from different patterns. A new 3D version of the technique that provides improved resolution and selectivity to help address cases with severe congestion was recently demonstrated. The experimental design and interpretation of data for the 3D technique are significantly more complicated than that for the 2D version. The purpose of this paper is to provide important information needed to plan, run, and interpret results from high-resolution coherent 3D spectroscopy experiments.

High-resolution coherent three-dimensional spectroscopy of Br2

In the past, high-resolution spectroscopy has been limited to small, simple molecules that yield relatively uncongested spectra. Larger and more complex molecules have a higher density of peaks and are susceptible to complications (e.g., effects from conical intersections) that can obscure the patterns needed to resolve and assign peaks. Recently, high-resolution coherent two-dimensional (2D) spectroscopy has been used to resolve and sort peaks into easily identifiable patterns for molecules where pattern-recognition has been difficult. For very highly congested spectra, however, the ability to resolve peaks using coherent 2D spectroscopy is limited by the bandwidth of instrumentation. In this article, we introduce and investigate high-resolution coherent three-dimensional spectroscopy (HRC3D) as a method for dealing with heavily congested systems. The resulting patterns are unlike those in high-resolution coherent 2D spectra. Analysis of HRC3D spectra could provide a means for exploring the spectroscopy of large and complex molecules that have previously been considered too difficult to study.

High resolution coherent 2D spectroscopy

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.

Analysis of polyatomic molecules using high resolution coherent two-dimensional spectroscopy: Application to nitrogen dioxide

The peak-sorting capabilities of high resolution coherent two-dimensional (2D) spectroscopy provide a new way of dealing with severe rotational congestion. This paper describes the application of this technique to the polyatomic molecule, NO(2). NO(2) is a primary component of photochemical smog and has a notoriously complex and congested spectrum that extends from the infrared to the ultraviolet regions. This spectrum is infamous for having an unusually high density of peaks and very few regular patterns. However, the coherent 2D spectrum of NO(2) shows a network consisting of numerous X-shaped patterns that mark the locations of vibronic origins. This paper describes how peak sorting leads to the formation of such patterns and how peak coupling can be used to conduct a rotational analysis of congested areas in the visible spectrum of NO(2).

Propagation, beam geometry, and detection distortions of peak shapes in two-dimensional Fourier transform spectra

Using a solution of Maxwell's equations in the three-dimensional frequency domain, femtosecond two-dimensional Fourier transform (2DFT) spectra that include distortions due to phase matching, absorption, dispersion, and noncollinear excitation and detection of the signal are calculated for Bloch, Kubo, and Brownian oscillator relaxation models. For sample solutions longer than a wavelength, the resonant propagation distortions are larger than resonant local field distortions by a factor of approximately L/lambda, where L is the sample thickness and lambda is the optical wavelength. For the square boxcars geometry, the phase-matching distortion is usually least important, and depends on the dimensionless parameter, L sin(2)(beta)Deltaomega/(nc), where beta is the half angle between beams, n is the refractive index, c is the speed of light, and Deltaomega is the width of the spectrum. Directional filtering distortions depend on the dimensionless parameter, [(Deltaomega)w(0) sin(beta)/c](2), where w(0) is the beam waist at the focus. Qualitatively, the directional filter discriminates against off diagonal amplitude. Resonant absorption and dispersion can distort 2D spectra by 10% (20%) at a peak optical density of 0.1 (0.2). Complicated distortions of the 2DFT peak shape due to absorption and dispersion can be corrected to within 10% (15%) by simple operations that require knowledge only of the linear optical properties of the sample and the distorted two-dimensional spectrum measured at a peak optical density of up to 0.5 (1).