Knowledge Bank

A simple model previously used to describe vibrations of $homonuclear1$ and $heteronuclear2$ diatomic molecules has been extended to symmetric stretching vibrations of polyatomic $XYn$ molecules. The model consists of a system of point charges: First, a static set $+eZi$ representing the nuclci and core electrons; and second, a set -eq representing the valence electrons, assumed to move free-electron-like in the bonds. For a symmetric breathing'' motion of the nuclei, the Born-Oppenheimer electronic energy is the sum of kinetic plus potential energy, $W(S) = T(S) + V(S)$, where S is the dimensionless scale parameter describing the symmetric motion. The kinetic energy T is modeled as a sum of particle-in-a-box energies, wherein each bond charge, q, moves independently in a box of length $\nu$/S. The potential energy V is modeled as a sum of all possible coulomb attractions and repulsions among the point charges. A symmetric stretching force constant'' is then defined, $Kaym=(d2W/dS2)eq$, and used to relate the model parameters q and $\nu$ to molecular structure data and force constants. Using this data as input, values of q and $\nu$ have been calculated for some $30XYn$ molecules, in symmetries $D\infty h,C2\nu ,C3\nu ,D2h$ and $Td$. Values of q are found to be reasonable measures of bond order. Values of $\nu$ are found to depend on the positions of the constituent atoms (X and Y) in the periodic chart, and are interpreted as measuring the core radii of the atoms.