The Band Spectra of the Hydrides of Lithium. Part III. Potential Curves and Isotope Relations

Abstract

The empirical band spectrum rho-values, ${\ensuremath{\rho}}^{*}$, as computed from the constants of LiH and LiD depart markedly from the ratio of the reduced masses, $\ensuremath{\rho}={(\frac{\ensuremath{\mu}}{{\ensuremath{\mu}}^{i}})}^{\frac{1}{2}}$. The isotope discrepancy, (${\ensuremath{\rho}}^{*}\ensuremath{-}\ensuremath{\rho}$) is positive for the 11 band constants measured for the ground state and negative for 10 of the 13 in the upper state. By using Dunham's equations, the anharmonicity constants ${a}_{1}, {a}_{2}\ensuremath{\cdots}{a}_{6}$ are computed for the ground state and the effect of anharmonicity on the isotope ratio calculated. In only 2 cases out of 5 does this reduce the isotope discrepancy and then by amounts from 6 to 22 percent. In the upper state the anharmonicity constants must be got by a laborious approximation process. It is shown that the resulting set of $a$ values accounts quite satisfactorily for both the sign and value of the 9 band constants, which have been previously reported as abnormal. This well-known abnormality can therefore not be ascribed in any significant measure to $L$ uncoupling. The Dunham corrections further reduce the isotope discrepancy in 4 out of 5 cases by an average of about 25 percent. The dissociation energies (Morse) are found to be for LiD, ${\mathrm{D}}_{0}$\ensuremath{''} = 2.53, ${\mathrm{D}}_{0}$\ensuremath{'} = 1.15 volts and for LiH ${\mathrm{D}}_{0}$\ensuremath{''} = 2.54 and ${\mathrm{D}}_{0}$\ensuremath{'} = 1.18 volts (all \ifmmode\pm\else\textpm\fi{}0.2 volt and measured from the $v=0$ level).