# QUADRATIC HERMAN-WALLIS FACTORS FOR THE FUNDAMENTALS OF LINEAR MOLECULES

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 Title: QUADRATIC HERMAN-WALLIS FACTORS FOR THE FUNDAMENTALS OF LINEAR MOLECULES Creators: Watson, J. K. G. Issue Date: 1987 Publisher: Ohio State University Abstract: The effect of vibration-rotation interactions on the intensities of allowed lines of linear molecules can be represented by the Herman-$Wallis^{1}$ correction factors $F^{PR} = [1 + a_{1}m + a_{2}^{PR}m^{2}]^{2}, m = J+1 (R branch), -J (P branch), F^{Q}= [1 + a^{Q}_{2}J(J+1)]^{2}$. For fundamental bands the $a_{1}$ and $a_{2}$ coefficients correspond to the terms $M_{12}$ and $M_{13}$ of the effective dipole moment $operator^{2}$. In this work explicit formulas are derived for the $a_{2}$ coefficients in the fundamentals of linear molecules. The calculation of these parameters requires up to cubic potential derivatives and quadratic dipole derivatives. A comparison is made between the calculated values for the fundamentals of carbon dioxide and those recently measured by $Johns^{3}$. Description: $^{1}$ R. Herman and R. F. Wallis, J. Chem. Phys. 23, 637 (1955). $^{2}$ M. R. Aliev and J. K. G. Watson, in Molecular Spectroscopy: Modern Research'' (ed. K. Narahari Rao), Vol. III (Academic Press, 1985). $^{3}$ J. W. C. Johns, paper presented at this symposium. Author Institution: Herzberg Institute of Astrophysics, National Research Council of Canada URI: http://hdl.handle.net/1811/17317 Other Identifiers: 1987-TB-8