Simple Bond-Charge Model for Potential-Energy Curves of Heteronuclear Diatomic Molecules

Abstract

A model for the vibrational potential‐energy functions of diatomic molecules, previously applied to homonuclear molecules only, is extended to 54 heteronuclear diatomic molecules in 93 different electronic states. Experimental $R_e$ and $k_e$ values are used to determine for each species the empirical bond‐charge and bond‐length parameters, $q$ and $\nu$ , in the homopolar model potential $${\mathrm{W\hspace{0.17em}=\hspace{0.17em}W}}_0{\mathrm{\hspace{0.17em}+\hspace{0.17em}(e}}^2{\mathrm{\hspace{0.17em}/\hspace{0.17em}R)\; (Z}}^2{\text{\hspace{0.17em}−\hspace{0.17em}4Z}}_q{\text{)\hspace{0.17em}+\hspace{0.17em}(1\hspace{0.17em}/\hspace{0.17em}R}}^2{\mathrm{)[(h}}^2{\text{\hspace{0.17em}/\hspace{0.17em}8m) (q\hspace{0.17em}/\hspace{0.17em}ν}}^2\mathrm{].}$$ This potential is known to be reasonably accurate for $R$ near $R_e$ . The molecular virial theorem requires that the term proportional to $R^{\text{−1}}$ represent electronic potential energy; this is modeled by supposing that an electronic charge $\mathrm{-qe}$ is at the bond center, and a net charge of $\mathrm{+Ze}$ is at each nucleus, with $\text{q\hspace{0.17em}=\hspace{0.17em}2Z}$ for neutral molecules. The virial theorem also requires that the term proportional to $R^{\text{−2}}$ represent electronic kinetic energy; this is modeled by supposing that the $q$ electrons move free‐electron‐like in a one‐dimensional box of length $\mathrm{\nu R}$ . As in the homonuclear case, the parameters $\nu$ are found to vary little from state to state in a given molecule, or through a given row in the periodic table. It is shown that heteronuclear ${\nu }_{\mathrm{AB}}$ values can be estimated from homonuclear $\nu$ values using formulas like ${\nu }_{\mathrm{AB}}{\mathrm{(R}}_{\mathrm{AA}}{\mathrm{\hspace{0.17em}+\hspace{0.17em}R}}_{\mathrm{BB}}{\mathrm{)\hspace{0.17em}=\hspace{0.17em}\nu }}_{\mathrm{AA}}{R}_{\mathrm{AA}}{\mathrm{\hspace{0.17em}+\hspace{0.17em}\nu }}_{\mathrm{BB}}{R}_{\mathrm{BB}}$ , and it is shown further that ${\nu }_{\mathrm{AB}}$ values are measures of the core (ionic) radii of atoms A and B in a molecule. Values of the parameters ${\text{q\hspace{0.17em}=\hspace{0.17em}(4R}}_e^3{k}_e{\text{\hspace{0.17em}/\hspace{0.17em}7e}}^2{)}^{\text{1/2}}$ correlate nicely with other, more conventional measures of bond population or bond order. Alternative, more complicated, heteropolar models for a heteronuclear diatomic molecule are examined. These models involve different charge parameters $Z_A$ and $Z_B$ on the two nuclei, and location of the bond charge $q$ elsewhere than at the bond center. Predicted $q$ and $\nu$ values, and hence the vibrational force constants, are shown to be insensitive to choice of the model. Values for the molecular electric dipole and quadrupole moments are more sensitive to the model, however. Arguments are presented for preferring the homopolar model, with $Z_A{\mathrm{\hspace{0.17em}=\hspace{0.17em}Z}}_B$ and $q$ at the bond center, as the zero‐order model for describing molecular vibrations.