Fundamental vibrational transitions of the H3 e H4 e+ and L7 iH+ ions calculated without assuming the Born-Oppenheimer approximation and with including leading relativistic corrections

Very accurate variational calculations of the fundamental pure vibrational transitions of the H3 e H4 e+ and L7 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 10000 Gaussian functions are used for each state. It is shown that the experimental H3 e H4 e+ fundamental transitions is reproduced within 0.06 cm-1 by the calculations. A similar precision is expected for the calculated, but still unmeasured, fundamental transition of L7 iH+. Thus, three-electron diatomic systems are calculated with a similar accuracy as two-electron systems.