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Diatomic Spectral Database, Equilibrium Internuclear Distances
7. Equilibrium Internuclear Distances
When precise values for the Dunham coefficients, Ylj, are obtained from experiment, the equilibrium internuclear distance can be determined from the equilibrium rotational constant Be. Dunham [3] derived the following relationship between Y01 and Be:
$$ Y_{01} = B_{\rm e} + \left({\displaystyle \frac{B_{\rm e}^3}{4\omega_{\rm e}^2}}\right)
\left[30+28a_1 +21\left(a_1^2 + a_1^3\right)
- 18a_2 - 46a_1a_2 + 30a_3 \right] $$
(eq 27)
where the ai are the anharmonic potential constants that can be evaluated from the higher Yij coefficients. The equilibrium internuclear distance is then expressed as:
$$ r_{\rm e} = \left( {\displaystyle \frac{h}{8\pi^2 \mu_{\rm r} B_{\rm e}}} \right)^{1/2} $$
(eq 28)
Since Dunham's treatment utilizes the Born-Oppeniheimer approximation, the value of Be must be modified for breakdown of this approximation. Several methods have been developed for handling these corrections; the most important are those of Rosenblum et al. [58008], Bunker [17], and Watson [73023].