Dirac-Fock calculation for H, H2+ and H2 in a strong magnetic field by the Hermitian basis of B-splines

A two-dimensional, fully numerical approach to the solution of four-component Dirac-Fock equation using the moderately long Hermitian basis of B-splines is applied to H, H2+ and H2 in a strong magnetic field. The geometric parameters, including different behavior of wave-functions relativistic components are analyzed. The accuracy of the solutions as a function of the basis lenght is estimated. The relativistic corrections are calculated by transformation of the matrix equations to the equations for large relativistic components. Application of the finite-element method to solution of the Dirac-Fock equation without supplementary assumption about exchange in case of the H2 excited states is discussed. The maximum localization of the basis functions provides applicability of the quadrature formulae for five-dimensional two-electron integral calculations within reasonable period.