  The use of Slater-type spinor orbitals in algebraic solution of the Dirac
equation is investigated. The one- and two-center integrals constitute the
matrix elements arising in generalized eigenvalue equation for one-electron
atoms and molecules are evaluated over Slater-type spinor orbitals via
ellipsoidal coordinates. These integrals are calculated through numerical
global-adaptive method with Gauss-Kronrod numerical integration extension. The
calculations are performed for electronic structure of ground and excited
states of one-electron atoms and diatomic molecules. The screening constants
are allowed to be variationally optimum values for given nuclear separation.
The obtained results are compaired with the results those found in the
literature. The procedures discussed in this work are capable of yielding
highly accurate relativistic two-center one-electron integrals for all ranges
of orbital parameters. Besides provides an efficient way to overcome the
problems that arise in relativistic calculations.
