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Expectation values of geometric structure parameters δ (r) , δ (r 12) , 1 r , r , r 2 , 1 r 12 , r 12 , r 12 2 , r < , r > , cos θ 12 , θ 12 for ground state, singlet and triplet singly excited 1 n 2 s 1 , 3 S e , 1 s n p 1 , 3 P o states with n up to 5 of helium were calculated in detail with Hylleraas-B-spline basis. Our results of δ (r) and δ (r 12) for helium ground state have 14 and 6 significant digits, respectively, and have at least 9 significant digits for other parameters. Expectation values of δ (r) , 1 r , 1 r 12 have at least 9 significant digits and expectation values of r < , r > reach 8 significant digits for singly excited S and P states. Expectation values of cos θ 12 , θ 12 are in coincidence with data in the previous work. Our results from independent calculation with Hylleraas-B-spline method are in good agreement with the previous works. [ABSTRACT FROM AUTHOR]

We multiply the anisotropic Gaussian atomic orbital by a field-dependent gauge phase to describe the wave function for the hydrogen molecular ion in non-aligned magnetic fields. With the kind of basis set, the convergence of the total energy at the equilibrium distance for the 1 state is much improved compared to the same atomic orbital without the gauge phase. For 2.35 × 10 ≤ B ≤ 10 T, better total energies of the 1 state at the corresponding equilibrium are obtained for the deviations 15°-90° of the magnetic field relative to the molecular axis. The result also shows that, there is a transition of the equilibrium configuration from the vertical orientation to the parallel orientation with increasing field strength. [ABSTRACT FROM AUTHOR]