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The use of Slater-type spinor orbitals in algebraic solution of the Diracequation is investigated. The one- and two-center integrals constitute thematrix elements arising in generalized eigenvalue equation for one-electronatoms and molecules are evaluated over Slater-type spinor orbitals viaellipsoidal coordinates. These integrals are calculated through numericalglobal-adaptive method with Gauss-Kronrod numerical integration extension. Thecalculations are performed for electronic structure of ground and excitedstates of one-electron atoms and diatomic molecules. The screening constantsare allowed to be variationally optimum values for given nuclear separation.The obtained results are compaired with the results those found in theliterature. The procedures discussed in this work are capable of yieldinghighly accurate relativistic two-center one-electron integrals for all rangesof orbital parameters. Besides provides an efficient way to overcome theproblems that arise in relativistic calculations.

The use of Slater-type spinor orbitals in algebraic solution of two-center Dirac equation