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The universal variational expansion for the non-relativistic three-bodysystems is explicitly constructed. Three-body universal expansion can be usedto perform highly accurate numerical computations of the bound state spectra inarbitrary three-body systems, including Coulomb three-body systems witharbitrary particle masses and electric charges. Our main interest is related tothe adiabatic three-body systems which contain one bound electron and two heavynuclei of hydrogen isotopes: the protium $p$, deuterium $d$ and tritium $t$. Wealso consider the analogous (model) hydrogen ion ${}^{\infty}$H$^{+}_2$ withthe two infinitely heavy nuclei.  PACS number(s): 36.10.-k and 36.10.Dr

the european physical journal. d, atomic, molecular and optical physics/the european physical journal. d, atomic, molecular, optical and plasma physics

Highly accurate bound state calculations of the two-center molecular ions by using the universal variational expansion for three-body systems