BREAKDOWN OF THE BORN-OPPENHEIMER APPROXIMATION IN THE LEAST SQUARES FITTING OF SPECTROSCOPIC LINE POSITIONS: THE $X^{1}\Sigma^{+}$ STATE OF HYDROGEN CHLORIDE
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Date
1985
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Ohio State University
Abstract
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}.$^{1}$ on $H_{2}$ and $D0_{2}$, in which effective, but constant, vibrational and rotational reduced masses, $\mu_{v}$ and $\mu_{r}$, were employed. Following the more recent formalism of $Watson^{2}$, the effective vibration-rotation Hamiltonian for a $^{1}\Sigma$ 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 $V_{eff}(R)$ 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 $V_{eff}(R)$ and g(R) from measured line positions. This procedure, which is based on the ``Inverse Perturbation Analysis” method of Kosman and $Hinze^{3}$, 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 $v \leq$ 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 $\leq v \leq$ 17 from the V $\rightarrow$ X $system^{4}$. The effective Hamiltonians, in the form of Eq. [1], are found to reproduce $\sim$2000 line positions to within the associated estimated absolute errors.
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$^{1}$P.R. Bunker, C.J. McLarnon and R.E. Moss, Mol. Phys. 33, 425 (1977). $^{2}$J.K.G. Watson, J. Mol. Spectrosc. 80, 411 (1980). $^{3}$W.E. Kosman and J. Hinze, J. Mol. Spectrosc. 56, 93 (1975). $^{4}$J.A. Coxon, U.K. Roychowdhury and A.E. Douglas, to be published.d
Author Institution: Department of Chemistry, Dalhousie University
Author Institution: Department of Chemistry, Dalhousie University