Benchmark values for molecular three-center integrals arising in the Dirac equation

Abstract: The authors in their previous papers obtained compact, arbitrarily accurate expressions for two-center one- and two-electron relativistic molecular integrals expressed over Slater-type orbitals. In this present study, the accuracy limits of given expressions is examined for three-center nuclear attraction integrals, which are the first integral set do not have analytically closed form relations. They are expressed through new molecular auxiliary functions obtained via Neumann expansion of Coulomb interaction. The numerical global adaptive method is used to evaluate these integrals for arbitrarily values of orbital parameters, quantum numbers. Several methods, such as Laplace expansion of Coulomb interaction, single-center expansion, Fourier transformation method, have been performed in order to evaluate these integrals considering the values of principal quantum numbers in the set of positive integer numbers. This is the first attempts to study the three-center integrals without any restrictions on quantum numbers and in all ranges of orbital parameters.