  Three-center nuclear attraction integrals with Slater type orbitals (STOs)
appearing in the Hartree-Fock-Roothaan (HFR) equations for molecules are
evaluated using one-range addition theorems of STOs obtained from the use of
complete orthonormal sets of -exponential type orbitals (-ETOs), where . These
integrals are investigated for the determination of the best with respect to
the convergence and accuracy of series expansion relations. It is shown that
the best values are obtained for . The convergence of three-center nuclear
attraction integrals with respect to the indices for is presented. The final
results are expressed through the overlap integrals of STOs containing . The
hermitian properties of three-center nuclear attraction integrals are also
investigated. The algorithm described in this work is valid for the arbitrary
values of, and quantum numbers, screening constants and location of orbitals.
The convergence and accuracy of series are tested by calculating concrete
cases. It should be noted that the theory of three-center nuclear attraction
integrals presented in this work is the extension of method described in our
previous paper for to the case of (I.I. Guseinov, N. Seckin Gorgun and N. Zaim,
Chin. Phys. B 19 (2010) 043101-1-043101-5).
