Basis set expansions of relativistic molecular wave equations

The unboundedness of the Dirac hamiltonian, the singular (or nearly singular) behaviour of the spinors at the nuclei and the strong coupling of the four spinor components causes difficulties when solving relativistic wave equations by the linear expansion technique. The solutions are sensitive to variational collapse; spurious solutions appear near the ground state energy. The situation is analysed. A quasi-unitary transformation of the Dirac equation in spinor space is proposed, which results in better behaved matrix representations. Numerical calculations on hydrogen-like atoms are used for comparison with the standard Dirac equation and the second order equation of Wallmeier and Kutzelnigg. Comments on the choice of basis sets are given.