INTEGRATED INFRARED INTENSITIES: RELATION TO OTHER. MOLECULAR CONSTANTS
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Date
1976
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Ohio State University
Abstract
A simple matrix formulation of the absolute infrared intensities $(T_{i})$ has been reported only recently by Mohan and M\""{u}ller, But, unfortunately, the matrices related to the absolute intensities $(T_{i})$ or the Integrated intensities $(A_{i})$ (i stands for the fundamental) are singular. Hence, no secular equation could be derived in this case. However, sum rule type relations involving the integrated absorption intensities $(A_{i})$ and other molecular constants could be developed. It is the aim of this communication to report the use of the matrix notation in developing relations connecting $A_{i}$ with the other molecular constants. The relations thus formulated have been explored to see whether a unique set of values for the derivatives of the dipole moment with respect to the symmetry coordinates (i.e., $\partial \mu/ \partial S_{i}$) could be computed when the values of the other molecular constants are known. In order to serve as a guide in seeing whether the quantum mechanical calculations lead to physically and mathematically meaningful results for the $(\partial \mu/ \partial S_{i})$ quantities, the extremal properties of $(\partial \mu/ \partial S_{i})^{2}$ and of $\Sigma_{i}(\partial \mu/ \partial S_{i})^{2}$ are discussed in detail. The matrix notation has also been used to formulate a simple isotopic rule involving $A_{i}$ (for each index i separately), which is valid for symmetric isotopic substitutions involving heavy and very heavy atoms.
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Author Institution: Institute of Chemistry, University of Dortmund; Laboratoire de Recherches Optiques, Facult\'{e} des Sciences