A SIMPLE POTENTIAL ENERGY FUNCTION FOR $CO_{2}$ VIBRATIONAL ANALYSIS

Abstract

An accurate theoretically motivated function for the vibrational potential energy surface of linear $AB_{2}$ triatomic molecules is tested on $CO_{2}$. The working formula for the potential energy W is $$ W(R_{1},R_{2},\Theta) = W_{D}(R_{1})+W_{D}(R_{2})+A/|\mathop {R}_{\sim}{_{3}|}^{N} -B/(R_{1} + R_{2})^{N}$$ where $R_{1}$ and $R_{2}$ are distances from the central nucleus to the other two nuclei, $\Theta$ is the apex angle, $W_{D}(R_{1})$ and $W_{D}(R_{2})$ are potential functions for the diatomic molecules, $R_{3}$ is the vector sum $R_{1} + R_{2}$, and A, B, and N are constants.