# BOND CHARGE MODEL FOR VIBRATIONS OF $XY_{n}$ MOLECULES.

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 Title: BOND CHARGE MODEL FOR VIBRATIONS OF $XY_{n}$ MOLECULES. Creators: Borkman, R. F. Issue Date: 1969 Publisher: Ohio State University Abstract: A simple model previously used to describe vibrations of $homonuclear^{1}$ and $heteronuclear^{2}$ diatomic molecules has been extended to symmetric stretching vibrations of polyatomic $XY_{n}$ molecules. The model consists of a system of point charges: First, a static set $+eZ_{i}$ 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, $K_{aym} = (d^{2}W/dS^{2})_{eq}$, 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 $30 XY_{n}$ molecules, in symmetries $D_{\infty h}, C_{2\nu}, C_{3\nu}, D_{2h}$ and $T_{d}$. 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. Description: $^{1}$ R. G. Parr and R. F. Borkman, J. Chem. Phys. 49, 1055 (1968). $^{2}$ R. F. Borkman, G. Simons and R. G. Parr, J. Chem. Phys. 50, 58 (1969). Author Institution: School of Chemistry, Georgia Institute of Technology URI: http://hdl.handle.net/1811/15679 Other Identifiers: 1969-D-12