  It is shown that the molecular ion ${\rm H}^{++}_3$ does not exist in a form
of the equilateral triangle. To this end, a compact variational method is
presented which is based on a linear superposition of six specially tailored
trial functions containing non-linear parameters. Careful optimization of a
total of fifteen parameters gives consistently lower variational results for
the electronic energy than can be obtained with standard methods of quantum
chemistry even with huge basis sets as large as mcc-pV7Z.
