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  Home > JCE Print > Journal of Chemical Education > Issues > 2005  > January  >
Information • Textbooks • Media • Resources
Global Least-Squares Analysis of the IR Rotation–Vibration Spectrum of HCl
Joel Tellinghuisen
Department of Chemistry, Vanderbilt University, Nashville, TN 37235
Cover
January 2005
Vol. 82 No. 1
p. 150
Abstract
The study of the IR rotation–vibration spectrum is a mainstay of the undergraduate laboratory curriculum in spectroscopy. Typical spectra consist of the fundamental and overtone bands for H35Cl and H37Cl (and sometimes D35Cl and D37Cl). These can be analyzed by least-squares fitting (i) one vibrational level at a time (using the method of combination differences), (ii) one band at a time, (iii) one isotopomer at a time, and (iv) both bands of both (or all) isotopomers simultaneously. The last two approaches involve the simultaneous fitting of two or more similar data sets and yield statistically optimal results. Procedures for doing such fits are illustrated for the data presentation and analysis program KaleidaGraph, with emphasis on the use of the program’s Macro Library for defining components of complex-fit models. Such methods greatly enhance operator efficiency and make global analysis truly feasible for students, as the only effort required of the user is (i) importing or entering the data and (ii) entering the fit-definition functions in very nearly their algebraic form. The article includes a comprehensive summary of standard notation for energy levels in diatomic molecules, a critique of methods used to estimate the key molecular parameters, and a discussion of subtle issues involved in rounding least-squares fit parameters for presentation.
Supplement
Global-fitting examples are available.
*  Contents JCE2005p0150W.doc (Microsoft Word)
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*  Citation
 Tellinghuisen, Joel. J. Chem. Educ. 2005 82 150.
*  Keywords
 Computer Assisted Instruction; Computer-Based Learning; Gases; Laboratory Instruction; Numerical Methods; Physical Chemistry; Spectroscopy; Statistics / Data Analysis; Upper-Division Undergraduate
*  History
 Created:
Last Updated:		 November 29, 2004
December 10, 2004
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