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The mass-correction functions in the second-order non-adiabatic Hamiltonianare computed for the $^4$He$^+_2$ molecular ion using the variational method,floating explicitly correlated Gaussian functions, and a generalcoordinate-transformation formalism. When non-adiabatic rovibrational energylevels are computed using these (coordinate-dependent) mass-correctionfunctions and a highly accurate potential energy and diagonal Born-Oppenheimercorrection curve, significantly improved theoretical results are obtained forthe nine rotational and two rovibrational intervals known from high-resolutionspectroscopy experiments.

Non-adiabatic mass-correction functions and rovibrational states of $^4$He$_2^+$ ($X\ ^2\Sigma_\text{u}^+$)