## INFRARED BAND SHAPES I. INTRODUCTION

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Ohio State University##### Abstract:

The infrared spectrum of a polyatomic molecule contains a large amount of information which has been untapped. Under favorable conditions it is possible to obtain some of it. For example, the shape of a band corresponding to a degenerate mode can yield the Coriolis coupling constant and the difference in the moments of inertia ($B^{\prime} -B^{\prime\prime}$, etc.). The latter may also be obtained for some nondegenerate vibrations. The details will be discussed in the two succeeding papers (II and III). If the shape of an infrared band has been determined by the methods above, the single parameter which determines its size, i.e. which superimposes the calculated and experimental curve, is the integrated absorption coefficient $\alpha$. This provides a possible alternate experimental method for $\alpha$. To do this it is necessary to measure (I($v$) (and $I^{\circ}(\nu)$ ). An infrared spectrometer measures $T(\nu^{\prime}$) while the theory deals with $I(\nu^{\prime}$). These are related by the well known expression {T}(\nu^{\prime})=\int{I}(\nu){g}(\nu, \nu^{\prime}){d}\nu where ${g}(\nu, \nu^{\prime})$ is the slit function. If one measures ${g}(\nu, \nu^{\prime})$ experimentally, one might solve the above integral equation for $I(\nu$). This problem will be discussed in greater detail in paper IV. A knowledge of $I(\nu$) (and $IO(\nu)$) determines $\alpha(\nu)$. Its relation to the transition probabilities involves the pressure broadening function. It will be shown that for a band consisting of groups of superimposed lines, where the groups are separated by $\Delta\nu^{\circ}$ \alpha(\nu)={kB}(\nu)/\Delta\nu^{\circ} if (1) the pressure is great enough that $\Delta\nu_{1/2}>>\Delta\nu^{0}$ and (2) the pressure is sufficiently low that B($\nu$) may be considered linear in the interval $\Delta\nu_{1/2}$. Here $\Delta\nu_{1/2}$ is the width at half-height of the pressure broadening function and $B(\nu)=\Sigma_{n}{N}_{n}{B}_{{nn}^{\prime}}(\nu)$ is the probability sum.

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Author Institution: Department of Chemistry, Purdue University

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