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Spectroscopy from Space pp 107–129Cite as

Determination of Molecular Parameters from Experimental Spectra

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Part of the book series: NATO Science Series ((NAII,volume 20))

Abstract

When fitting the rotation-vibrational spectra we try to determine such a set of parameters x, [x i , i= 1, … m)] that would give the best agreement between the observed and calculated frequencies of transitions y, [y j , j = 1, …n] between the rotation-vibrational energy levels . In most cases the relation between the two sets is nonlinear

$$ {y_{j}} = {F_{j}}\left( {{x_{1}},...{x_{m}}} \right), $$
(1)

and we have to apply the iteration method, starting with some initial estimate of the parameters x 0, which upon substituting in Eq. (1) provides a set of calculated values y calc. Assuming that our initial estimate is good we can use the Taylor expansion

$$ {y^{{^{{\exp }}}}} - {y^{{{\rm{calc}}}}} = J\Delta x, $$
(2)

to linearize the relation between y and x. In Eq. (2) the rectangular matrix J has dimension (n × m), its elements are the derivatives

$$ {J_{{ji}}} = {\left( {\frac{{\partial {F_{j}}}}{{\partial {x_{i}}}}} \right)_{{x = {x^{0}}}}}, $$
(3)

and

$$ \Delta x = x - {x^{0}}. $$
(4)

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Author information

Authors and Affiliations

  1. Laboratoire de Physique de Lasers, Atomes and Molécules, UMR CNRS 8523, Université de Lille I, Bâtiment P5, F-59655, Villeneuve d’Ascq, France

    J. Demaison

  2. Department of Physical Chemistry, Faculty of Pharmacy, Comenius University, 832 32, Bratislava, Slovakia

    K. Sarka

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  1. J. Demaison
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Editors and Affiliations

  1. CNRS, Université de Lille I, Lille, France

    Jean Demaison

  2. Comenius University, Bratislava, Slovakia

    Kamil Sarka

  3. Jet Propulsion Laboratory, California Institute of Technology, Pasadena, USA

    Edward A. Cohen

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Demaison, J., Sarka, K. (2001). Determination of Molecular Parameters from Experimental Spectra. In: Demaison, J., Sarka, K., Cohen, E.A. (eds) Spectroscopy from Space. NATO Science Series, vol 20. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0832-7_7

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  • DOI: https://doi.org/10.1007/978-94-010-0832-7_7

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