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Two Dimensional Symmetric Correlation Functions of the S Operator and Two Dimensional Fourier Transforms: Considering the Line Coupling for P and R Lines of Linear MoleculesThe refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS1 − S2 introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the ^S operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters' two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C2H2 broadened by N2. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.
Document ID
20140017666
Acquisition Source
Goddard Space Flight Center
Document Type
Reprint (Version printed in journal)
External Source(s)
doi:10.1063/1.4867417
Authors
Ma, Q. (Columbia Univ. New York, NY, United States)
Boulet, C. (Paris-Sud Univ. Orsay, France)
Tipping, R. H. (Alabama Univ. University, AL, United States)
Date Acquired
December 22, 2014
Publication Date
March 12, 2014
Publication Information
Publication: Journal of Chemical Physics
Publisher: AIP Publishing
Volume: 140
Issue: 10
Subject Category
Solid-State Physics
Report/Patent Number
GSFC-E-DAA-TN17559
Funding Number(s)
CONTRACT_GRANT: NSF 1228861
CONTRACT_GRANT: NNX14AB99A
CONTRACT_GRANT: DE-AC02-05CH11231
Distribution Limits
Public
Copyright
Public Use Permitted.
Keywords
infrared radiation
molecules
isotropy
Fourier transformation
formalism
correlation

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