## A NEW SIMPLE ISOTOPIC SUM RULE VALID FOR DIFFERENT MOLECULAR CONSTANTS

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Ohio State University##### Abstract:

A simple isotopic bum rule valid for individual shift of different molecular constants $M_{ij}$ (say, frequencies, Coriolis coupling constants, mean amplitudes of vibration, Bastiansen Merino shrinkage effects, integrated infrared intensities) is derived using the first order perturbation theory, i.e., one considers all and only all the first order terms in $\bigtriangleup L (\bigtriangleup L \neq 0)$ in the general expanded development of any equation. Let $\bigtriangleup M_{ij}^{(PP)}$ be the change in the molecular constant $M_{ij}$ pertaining to the symmetrical isotopic substitution of the sets of equivalent atoms 1 to p in the parent molecule (e.g., $X_{1} Y_{2} \cdots Z_{p} W_{q} \cdots /X_{1}^{*} Y_{2}^{*} \ldots Z_{p}^{*} W_{q} \ldots)$ and if the corresponding quantities representing cases where each set of atoms ""a"" is substituted by the isotopic one in succession $(e.g., X_{1} Y_{2} \ldots /X_{1}* Y_{2} \ldots$; $X_{1} Y_{2} \ldots /X_{1} Y_{2}* \ldots; X_{1} Y_{2} \ldots Z_{p} W_{q} \ldots /X_{1} Y_{2} \ldots Z_{p}* W_{q}\ldots)$, are $\bigtriangleup M^{a}_{ij}$ one has the isotopic sum rules, $$\bigtriangleup M_{ij}^{(pp)} = \Sigma ^{p} _{a}=1 \bigtriangleup M ^{(a)}_{ij}, \ \ ( \forall _{i}, \forall _{j}, \mbox{for each }p<n)$$ where n is the total number of sets of atoms. The isotopic sum rules are seen to hold good for symmetric substitution involving heavy atoms and serve as a very simple proof of the experimental data, especially in the cases of partial data as these rules are derived for individual molecular constants (e.g., none of the usual rules are applicable as for example the Teller-Redlich product rule).

##### Description:

Author Institution: Laboratoire de Recherches Optiques, Facult\'{e} des Sciences; Institute of Chemistry, University of Dortmund

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