Proof and Use of the Method of Combination Differences for Analyzing High-Resolution Coherent Multidimensional Spectra

Peter C Chen,Jeffrey Ehme

doi:10.3390/math8010044

Abstract

High-resolution coherent multidimensional spectroscopy is a technique that automatically sorts rotationally resolved peaks by quantum number in 2D or 3D space. The resulting ability to obtain a set of peaks whose J values are sequentially ordered but not known raises the question of whether a method can be developed that yields a single unique solution that is correct. This paper includes a proof based upon the method of combined differences that shows that the solution would be unique because of the special form of the rotational energy function. Several simulated tests using a least squares analysis of simulated data were carried out, and the results indicate that this method is able to accurately determine the rotational quantum number, as well as the corresponding Dunham coefficients. Tests that include simulated random error were also carried out to illustrate how error can affect the accuracy of higher-order Dunham coefficients, and how increasing the number of points in the set can be used to help address that.

Highlights

During the past two decades, coherent multidimensional spectroscopy (CMDS) has emerged as a powerful tool that can overcome the limitations of traditional one-dimensional techniques [1,2,3,4,5]
High-resolution coherent multidimensional spectroscopy (HRCMDS) is a form of CMDS that is designed to overcome congestion problems commonly found in the high-resolution spectra of gas-phase molecules [6]
The results show that combination differences can be used to determine accurate values for J

Summary

Introduction

During the past two decades, coherent multidimensional spectroscopy (CMDS) has emerged as a powerful tool that can overcome the limitations of traditional one-dimensional techniques [1,2,3,4,5]. High-resolution coherent multidimensional spectroscopy (HRCMDS) is a form of CMDS that is designed to overcome congestion problems commonly found in the high-resolution spectra of gas-phase molecules [6]. Gas molecules can yield spectra that contain a wealth of information (e.g., thousands or millions of peaks), but spectral congestion often precludes the ability to resolve and assign these peaks. Strategies for assigning resolved peaks in 1D spectroscopy have typically involved making initial guesses, trial and error, and pattern recognition.

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Conclusion