Knowledge Bank

Although it is well known that breakdown of the Born-Oppenheimer approximation has significant effects on the vibration-rotational eigenvalues of light molecules, rarely has full consideration of these effects been made in experimental determinations of the vibration-rotation Hamiltonians. A well known exception is the work of Bunker \emph{et al}.$\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}$ on $H2$ and $D02$, in which effective, but constant, vibrational and rotational reduced masses, $\mu v$ and $\mu r$, were employed. Following the more recent formalism of $Watson2$, the effective vibration-rotation Hamiltonian for a $\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}\Sigma$ state can be written as \begin{equation} \hat{H}{eff} = -(^{2}/2\mu{a})d^{2}/dR^{2} + [V_{eff} (R) + (\hbar^{2}/2\mu_{a} R^{2}){1 + g(R)}J(J+1)], \end{equation} where $Veff(R)$ is the effective internuclear potential taking account of adiabatic and J-independent non-adiabatic corrections, and g(R), from the remaining non-adiabatic terms, introduces non-mechanical J-dependent corrections to the eigenvalues of the rotating molecule, $\mu a$ is the atomic reduced mass. A direct least-squares fitting procedure has been developed for the determination of $Veff(R)$ and g(R) from measured line positions. This procedure, which is based on the ``Inverse Perturbation Analysis” method of Kosman and $Hinze3$, has been applied to the extensive data that are available for the ground state of HCl. The pure rotation and vibration-rotation data on levels $v\le$ 7, which include precise line positions from microwave and Fourier transform near-in spectroscopy, have been combined with the new and rotationally extensive data on levels 7 $\le v\le$ 17 from the V $\to$ X $system4$. The effective Hamiltonians, in the form of Eq. [1], are found to reproduce $\sim$2000 line positions to within the associated estimated absolute errors.