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# Diatomic Spectral Database, Equilibrium Internuclear Distances

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### 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].

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Created April 27, 2018, Updated November 15, 2019