Accurate One-Centre Method for Hydrogen Molecule Ions in Strong Magnetic Field

An accurate one-centre method for the hydrogen molecule ion is tested. The slow convergence and singularities at the nuclear positions that are problems in the general one-centre method are solved well by employing the optimal radial and angular B-spline basis. Therefore, the accuracy of the one-centre method is improved observably. For the ground state of the H₂⁺ in the free field, 7×10^-8 accuracy is obtained, which rivals the best one-centre calculation before. As a test, the nuclear distances and the total energies of the 1σ_g,u, 1π_u, 1δ_g,u and 2σ_g states of the H₂⁺ for the magnetic field strength B=1a.u. are also obtained. Compared to other results, five-digit accuracy at least can be arrived even for the antibonding states 1σ_u and 1δ_u, whose equilibrium distances R is very large