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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).
Using one-range addition theorems for noninteger n Slater type orbitals and Coulomb-Yukawa like correlated interaction potentials with noninteger indices obtained by the author with the help of complete orthonormal sets of exponential type orbitals,
Using the shift-operator technique, a compact formula for the Fourier transform of a product of two Slater-type orbitals located on different atomic centers is derived. The result is valid for arbitrary quantum numbers and was found to be numerically
Using the complete orthonormal sets of radial parts of nonrelativitistic exponential type orbitals (2,1, 0, 1, 2, ...) and spinor type tensor spherical harmonics of rank s the new formulae for the 2(2s+1)-component relativistic spinors useful in the
The series expansion formulae are established for the one- and two-center charge densities over complete orthonormal sets of exponential type orbitals introduced by the author. Three-center overlap integrals of appearing in these relations are expres
The new complete orthonormal sets of -Laguerre type polynomials (-LTP,) are suggested. Using Schrodinger equation for complete orthonormal sets of -exponential type orbitals (-ETO) introduced by the author, it is shown that the origin of these polyno