Nonparametric High-Resolution Coherent 3D Spectroscopy as a Simple and Rapid Method for Obtaining Excited-State Rotational Constants

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.