Vibrational Potential Functions for CO2, OCS, HCN, and N2O

Abstract

For linear triatomic molecules, ABC, a vibrational potential function is proposed and tested which has the form $${\mathrm{W\hspace{0.17em}=\hspace{0.17em}W}}_0\mathrm{\hspace{0.17em}+\hspace{0.17em}}\frac{W_1}{R_1}\mathrm{\hspace{0.17em}+\hspace{0.17em}}\frac{W_2}{R_2}\mathrm{\hspace{0.17em}+\hspace{0.17em}}\frac{W_{11}}{R_1^2}\mathrm{\hspace{0.17em}+\hspace{0.17em}}\frac{W_{22}}{R_2^2}\mathrm{\hspace{0.17em}+\hspace{0.17em}}\frac{W_{12}}{R_1{R}_2}\mathrm{\hspace{0.17em}+\hspace{0.17em}}\frac{W_{112}}{R_1^2{R}_2}\mathrm{\hspace{0.17em}+\hspace{0.17em}}\frac{W_{122}}{R_1{R}_2^2}\mathrm{\hspace{0.17em}+\hspace{0.17em}}\frac{W_G}{R_1{R}_2}\csc (\frac{1}{2}\mathrm{\gamma ),}$$ where $R_1$ and $R_2$ are $R_{\mathrm{AB}}$ and $R_{\mathrm{BC}},\mathrm{and}\gamma$ is the ABC angle. For CO₂, Potential (A) has five constants: $W_1{\mathrm{(=\hspace{0.17em}W}}_2{\mathrm{),\; W}}_{11}{\mathrm{(=\hspace{0.17em}W}}_{22}{\mathrm{),\; W}}_{12}{\mathrm{,\; W}}_{112}{\mathrm{(=\hspace{0.17em}W}}_{122}\mathrm{),}\mathrm{and}{W}_G$ , four of which are independent. In terms of these are calculated the 12 independent force constants in the most general valence‐force‐field potential through quartic terms. For HCN, OCS, and N₂O, Potential (A) has eight constants, six of which are independent. In terms of these are calculated the 19 independent valence‐force potential constants. Variations in (A) are discussed, as is its quantum theoretic basis. Physical arguments justify the form of all terms except $W_{112}{\mathrm{\hspace{0.17em}/\hspace{0.17em}R}}_1^2{R}_2$ and $W_{122}{\mathrm{\hspace{0.17em}/\hspace{0.17em}R}}_1{R}_2^2$ . The term involving $\gamma$ represents the dependence of electronic kinetic energy on bond angle.