Influence of a strong magnetic field on the hydrogen molecular ion using B-spline-type basis-sets

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 1σ_g and low excited states 1σ_u, 1π_g,u,1δ_g,u,2σ_g 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 1π_g, 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 1π_g 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 1σ_g, 1π_u, 1δ_g and antibonding states 1σ_u, 1π_g, 1δ_u 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.