Strategies for Interpreting High Resolution Coherent Multi- Dimensional Spectra Thresa A. Wells, Peter C. Chen and Zuri R. House Spelman College, Atlanta GA Benjamin R. Strangfeld Georgia Institute of Technology, Atlanta GA

NO 2 background Why so difficult to analyze? -The electronic spectrum of NO 2 is notorious for being complex and consisting of a high density of peaks, due to a series of conical intersections. -High density of peaks results in severe spectral congestion -New pattern recognition and new data analysis techniques needed -Near prolate asymmetric rotor -X-shaped clusters, B’=B’’

Example experimental 2D spectra

J”=1 J”=2 J”=3 J”=4 , cm -1  , cm -1  J”=1 J”=2 J”=3 J”=4  cm -1  , cm -1  B’=B” Boxes are concentric B’ ≠ B” Boxes are not concentric Resembles a “double” Fortrat parabolaX-shaped cluster Center Position Method(CPM)

Brief procedure description 1.Fbox: Algorithm written to find boxes within the experimental data set and list the points with the corresponding height, width and center position (origin) of the box it belongs to. 2.Group data by width 3.Using Excel to create a scatter plot of the center positions; each series representing a different box width. 4.Find clusters of center positions (i.e. clusters of center positions from different series). 5.Extract those cluster’s X and Y values, from the data set (not the plot) 6.Finally, plot the X and Y values. This should result in an individual X-shaped cluster.

Limitations of CPM/Why is 3D necessary? Resolving K=o vs K=1, even after using experimental values to form the assigned files for Fbox Congestion persists for 2D NO 2

From 2D 3D

3D NO 2 Results

New information 3D technique offers about NO 2

Determine the process responsible for resulting 3D Spectra or Process 1, OPO scan Process 4, OPO scan 44 44 44 44  OPO

Evidence to support process 4

Diagonal Level Information about vibrational level e Show resulting figure and table listing the experimental values and the Jost literature values for level e Based on B(4J+6) equation (explained further in the following talk) we are able to determine what the J quantum value is.

Deriving equation for diagonal line General equation for the output frequency of process 4: ω 4 = ω dye – ω SOPO + ω MOPO Y= mX +b Rearrange the equation for our experimental setup: MOPO on Y-axis and ω 4 on the X-axis Y = m X + b Where m=1

Y= m X+ b Y-intercept (top) Y-intercept (bottom match) Corresponding Jost value Delta

Determining the J value Using the delta between the main diagonal and it’s partner (secondary) diagonal, which is an average of about 9cm -1 *** B’’(4J+6)=9cm -1 ; where B’’ is approx. 0.4cm -1 Rearrange to solve for J: J = 4.125

hgfahgfa hgdahgda gdbagdba gfeagfea D technique due to process 1 or Process 4?

Process 4 is responsible for 2D technique as well

Summary 1.Things we know: -FWM process -Level e -J=4 -R-type plane 2. Things that require further study: -Why don’t all of the Vibronic Origins line up with the triangles? -Confirm K=o vs K=1

{Not using this slide}Center Position Method(CPM) 1.Next, a scatter plot of the center positions of the data is created in different series according to how many groups are generated. 2.After creating a scatter plot, then the entire data set is examined manually in order to find clusters of center positions (i.e. clusters of center positions from different series). 3.Then, each of these clusters is extracted from the data set (not the plot) and a new plot of the X and Y positions of each of the boxes in the X-shaped cluster is created, to determine if it appears to be an actual X-shaped cluster. 4.Finally, if after generating the plot, there appears to be more than one X-shaped cluster, repeat the procedure on this portion of the data. The goal is to extract each individual X-shaped cluster.