Fundamental vibrational transitions of theH3e H4e+andL7iH+ions calculated without assuming the Born-Oppenheimer approximation and with including leading relativistic corrections

Abstract

Very accurate variational calculations of the fundamental pure vibrational transitions of the $^{3}\text{H}\text{e}\text{ }{^{4}\text{H}\text{e}}^{+}$ and ${^{7}\text{L}\text{iH}}^{+}$ ions are performed within the framework that does not assume the Born-Oppenheimer (BO) approximation. The non-BO wave functions expanded in terms of one-center explicitly correlated Gaussian functions multiplied by even powers of the internuclear distance are used to calculate the leading relativistic corrections. Up to $10\text{ }000$ Gaussian functions are used for each state. It is shown that the experimental $^{3}\text{H}\text{e}\text{ }{^{4}\text{H}\text{e}}^{+}$ fundamental transitions is reproduced within $0.06\text{ }{\text{cm}}^{\ensuremath{-}1}$ by the calculations. A similar precision is expected for the calculated, but still unmeasured, fundamental transition of ${^{7}\text{L}\text{iH}}^{+}$. Thus, three-electron diatomic systems are calculated with a similar accuracy as two-electron systems.