Strategies for Interpreting High Resolution Coherent Multi-Dimensional Spectra

Thresa A. Wells, Peter C. Chen and Zuri R. HouseSpelman College, Atlanta GA

Benjamin R. StrangfeldGeorgia Institute of Technology, Atlanta GA

NO2 background

• Why so difficult to analyze?-The electronic spectrum of NO2 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

4w , cm-1

1w

, cm

-1 J”=1

J”=2J”=3J”=4

4w cm-1

1w

, cm

-1

B’=B”Boxes are concentric

B’ ≠ B”Boxes are not concentric

Resembles a “double” Fortrat parabola X-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.

16835 16840 16845 16850 16855 16860 16865 1687016200

16220

16240

16260

16280

16300

16320

16340

16360

16380

16400

Y1

16835 16840 16845 16850 16855 16860 1686516280

16290

16300

16310

16320

16330

16340

16350

Series1Series3Series5Series7Series9Series11Series13Series15Series17Series19Series21Series23Series25Series27Series29

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 NO2

From 2D 3D

564.5 564.7 564.9 565.1 565.3 565.5 565.7 565.9610.5

611

611.5

612

612.5

613

613.5

3D NO2 Results

New information 3D technique offers about NO2

Determine the process responsible for resulting 3D Spectra

or or

Process 1, OPO scan Process 4, OPO scan

w4 w4 w4 w4

wO

PO

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:

ω4 = ωdye – ωSOPO + ωMOPO

Y= mX +bRearrange the equation for our experimental setup:

MOPO on Y-axis and ω4 on the X-axis

Y = m X + bWhere m=1

Y= m X+ bY-intercept (top)

Y-intercept (bottom match)

Corresponding Jost value

Delta

8265 8274 8264.28 0.72

8183 8193 8178.27 4.73

8329 8338 8330.35 1.35

8204 8215 8218.84 3.84

8118 8127 8120.7 2.7

8095 8103 8093.61 1.39

8439 8452 8441.44 2.44

8046 8055 8046.44 0.44

8286 8295 8284.17 1.83

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

1 2 3 4

hgf

a

hg

d

a

g

dba

gfe

a 1 3 2 4 3 1 2 4 3 2 1 4 1 2 3 4

2D 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.