Completeness of a kinetically balanced Gaussian basis

It is shown that the exact relativistic wave function of the ground state of H-like ions can be expanded in a kinetically balanced even-tempered Gaussian basis. The error of the overlap integral between exact and approximate wave function depends as approximately n3/2+nu exp[-pisqrt(3/2+nu)n], with nu=-1+sqrt1-Z2/c2, on the size n of the basis, both for the large and the small components. Even the error of the energy has essentially the same dependence on n and decays only slightly slower than its nonrelativistic counterpart, which goes as approximately n3/2 exp[-pisqrt3n/2].