The Hydrogen Molecular Ion in Strong Fields Using the B-Spline Method

An accurate method combining the spheroidal coordinate and B-spline for H₂⁺ is tested. The equilibrium distances and the total energies of the states with |m|≤4 for the magnetic field strength γ=1 are given and compared with those obtained using different methods. Taking the advantages of the spheroidal coordinate and B-spline, a 10^?9–10^?12 accuracy is obtained for the energies of the states with |m|≤3, and a 10^?5–10^?7 accuracy for the equilibrium distances. There are seven significant digits for the energy of the state 1γ_g and four significant digits for 1γ_u, which are consistent with those obtained by the high-precision method. There are three significant digits for the equilibrium distances of the 1γ_g,u states, which are consistent.