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Title: Two dimensional symmetric correlation functions of the S-circumflex operator and two dimensional Fourier transforms: Considering the line coupling for P and R lines of linear molecules

The 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 iS{sub 1} − S{sub 2} 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-circumflex 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 coordinatemore » 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 C{sub 2}H{sub 2} broadened by N{sub 2}. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.« less
Authors:
 [1] ;  [2] ;  [3]
  1. NASA/Goddard Institute for Space Studies and Department of Applied Physics and Applied Mathematics, Columbia University, 2880 Broadway, New York, New York 10025 (United States)
  2. Institut des Sciences Moléculaires d'Orsay (ISMO), CNRS (UMR8214) et Université Paris-Sud Bât 350, Campus d'Orsay F-91405 (France)
  3. Department of Physics and Astronomy, University of Alabama, Tuscaloosa, Alabama 35487-0324 (United States)
Publication Date:
OSTI Identifier:
22253458
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 140; Journal Issue: 10; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CORRELATION FUNCTIONS; COUPLING; ENERGY GAP; FOURIER TRANSFORMATION; MATRIX ELEMENTS; QUANTUM NUMBERS; TENSORS; TWO-DIMENSIONAL CALCULATIONS