He3+2 and HeH2+ molecular ions in a strong magnetic field: The Lagrange-mesh approach

Accurate calculations for the ground state of the molecular ions He3+2 and HeH2+ placed in a strong magnetic field B≳102 a.u.B≳102 a.u. (≈2.35×1011 G≈2.35×1011 G) using the Lagrange-mesh method are presented. The Born–Oppenheimer approximation of zero order (infinitely massive centers) and the parallel configuration (molecular axis parallel to the magnetic field) are considered. Total energies are found with 9–10 s.d. The obtained results show that the molecular ions He3+2 and HeH2+ exist at B>100 a.u.B>100 a.u. and B>1000 a.u.B>1000 a.u., respectively, as predicted in Turbiner and López Vieyra (2007) [1] while a saddle point in the potential curve appears for the first time at B∼80 a.u.B∼80 a.u. and B∼740 a.u.B∼740 a.u., respectively.

► Application of the Lagrange-mesh method to two exotic molecular systems.
► He3+2 and HeH2+ exist at B>100 a.u.B>100 a.u. and B>1000 a.u.B>1000 a.u., respectively.
► Accurate results for the total energy.
► A saddle point in the potential appears at B∼80 a.u.B∼80 a.u. and B∼740 a.u.B∼740 a.u., respectively.