15min:

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 diatomic molecule can be written H = \sum_i (m _e/M_i) [p_rQ_i(r)p_r/2µ_C + \hbar²R_i(r)J(J+1)/2µ_Cr² + S_i(r)], where i refers to the two atoms, µ_C=M _AM _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 \beginequation R_i(r) = R_i(r) - 1øver rAⁱ(r), \qquad S_i(r) = S_i(r) + 1øver 2dV _BO(r)øverdrAⁱ(r), \qquad Aⁱ(r)=A₀ⁱ+\int_r _e^rQ_i(r')dr'. \endequation There remains the indeterminacy due to the arbitrary constant A₀ⁱ. 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 \beginequation \left[R_i+r _eøvera₀dS_iøverdr\right]_r _e, \endequation which involves the adiabatic correction to the potential S_i(r), can be determined. Here a₀= _e²/4B _e.