Abstract

An augmented version of the empirical Birge-Mecke rule ${\omega }_e/B_e\sim {\omega }_e{r}_e^2=\text{const}$, relating rotational and vibrational frequencies of molecular electronic states, derived by a semiclassical analysis of the motion of a Morse oscillator in the v = 0 level, is ${\mu }_A{\omega }_{\theta }{x}_{\theta }{r}_e^2=\left(h/2{\pi }^{2}c\right){\left(E_{\text{rot}}/E_{\text{vib}}\right)}^2\sim 135$. E_rot is the rotational energy excited by the time-averaged anharmonic oscillation, and E_vib is the zero-point energy ω_e/2. Comparison with the molecular data for 184 Morselike electronic states in Huber and Herzberg’s compilation¹ shows that the above equation holds well and that E_rot/E_vib = 1.141475 ± 0.030898. (12 min)

© 1987 Optical Society of America