INDETERMINACIES IN DIATOMIC BORN-OPPENHEIMER CORRECTIONS, WITH AN APPLICATION TO THE FITTING OF LiH DATA

\underline{JAMES K. G. WATSON}, Steacie Institute for Molecular Sciences, National Research Council of Canada, Ottawa, Ontario, Canada K1A 0R6.

The principal corrections to the Born-Oppenheimer Hamiltonian for a ^{1}Σ diatomic molecule can be written^{a} ΔH = ∑_{i}(m_{e}/M_{i})[p_{r}Q_{i}(r)p_{r}/2μ_{C} + h̄^{2}R_{i}(r)J(J + 1)/2μ_{C}r^{2} + S_{i}(r)], where i refers to the two atoms, μ_{C} = M_{A}M_{B}/(M_{A} + M_{B} − Cm_{e}) is a charge-modified reduced mass of the atoms for molecular electric charge C, and Q_{i}(r), R_{i}(r), and S_{i}(r) are isotope-independent functions that allow for non-adiabatic and adiabatic electronic effects. By a transformation of the Hamiltonian^{a} the Q_{i}(r) term can be eliminated, and R_{i}(r) and S_{i}(r) are replaced by

R̃_{i}(r) = R_{i}(r) − \frac{1}{r} A^{i}(r),  S̃_{i}(r) = S_{i}(r) + \frac{1}{2} \frac{dV_{BO}(r)}{dr} A^{i}(r),  A^{i}(r) = A_{0}^{i} + ∫_{r_{e}}^{r} Q_{i}(r′)dr′.  (1)

There remains the indeterminacy due to the arbitrary constant A_{0}^{i}. The present study of the fitting of the BO corrections for the isotopomers of the LiH molecule shows the way that this indeterminacy appears in numerical fits. The net effect is that the parameter R_{i}(r_{e}), which is a function of the equilibrium dipole moment and rotational g-factor of the molecule, cannot be determined from field-free frequency fits. Only the combination

[R_{i} + \frac{r_{e}}{a_{0}} \frac{dS_{i}}{dr} ]_{r_{e}} ,  (2)

which involves the adiabatic correction to the potential S_{i}(r), can be determined.^{b} Here a_{0} = ω_{e}^{2}/4B_{e}.

aJ. K. G. Watson, J. Mol. Spectrosc. 80, 411-21 (1980).

bJ. K. G. Watson, J. Mol. Spectrosc., in press