As an improvement on our previous work [J. Phys. B: At. Mol. Opt. Phys. 45 085101 (2012)], an accurate method combining the spheroidal coordinates and B-spline basis is applied to study the ground state 1σg and low excited states 1σu, 1πg,u,1δg,u,2σg of the H2+ in magnetic fields ranging from 109 Gs (1 Gs=10-4 T) to 4.414×1013 Gs. Comparing the one-center method used in our previous work, the present method has a higher precision with a shorter computing time. Equilibrium distances of the states of the H2+ in strong magnetic fields were found to be accurate to 3～5 significant digits (s.d.) and the total energies 6～11 s.d., even for some antibonding state, such as 1πg, which is difficult for the one-center method to give reliable results while the field strength is B≥q1013 Gs. For the large disagreement in previous works, such as the equilibrium distances of the 1πg state at B=109 Gs, the present data may be used as a reference. Further, the potential energy curves (PECs) and the electronic probability density distributions (EPDDs) of the bound states 1σg, 1πu, 1δg and antibonding states 1σu, 1πg, 1δu for B=1, 10, 100, 1000 a.u. (atomic unit) are compared, so that the different influences of the magnetic fields on the chemical bonds of the bound states and antibonding states are discussed in detail.
