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

Peter C. Chen and Jeffrey Ehme
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Peter C. Chen: Department of Chemistry and Biochemistry, Spelman College, 350 Spelman Lane SW, Atlanta, GA 30314, USA
Jeffrey Ehme: Department of Mathematics, Spelman College, 350 Spelman Lane SW, Atlanta, GA 30314, USA

Mathematics, 2020, vol. 8, issue 1, 1-12

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.

Keywords: combination differences; CMDS; rotational energy; spectroscopy; multidimensional; gas; quantum number; Dunham coefficient (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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