Evaluation of Self-Friction Three-Center Nuclear Attraction Integrals with Integer and Noninteger Principal Quantum Numbers n over Slater Type Orbitals

We have proposed a new approach to evaluate self-friction (SF) three-center nuclear attraction integrals over integer and noninteger Slater type orbitals (STOs) by using Guseinov one-range addition theorem in standard convention. A complete orthonormal set of Guseinov ψα exponential type orbitals (ψα-ETOs, α=2,1,0,-1,-2,…) has been used to obtain the analytical expressions. The overlap integrals with noninteger quantum numbers occurring in SF three-center nuclear attraction integrals have been evaluated using Qnsq auxiliary functions. The accuracy of obtained formulas is satisfactory for arbitrary integer and noninteger principal quantum numbers.

UNSYMMETRICAL AND SYMMETRICAL ONE-RANGE ADDITION THEOREMS FOR SLATER TYPE ORBITALS AND COULOMB–YUKAWA-LIKE CORRELATED INTERACTION POTENTIALS OF INTEGER AND NONINTEGER INDICES

Using one-center expansion relations for the Slater type orbitals (STOs) of noninteger principal quantum numbers in terms of integer nSTOs derived in this study with the help of ψa-exponential type orbitals (ψa-ETOs, a = 1, 0, -1, -2,…), the general formulas through the integer nSTOs are established for the unsymmetrical and symmetrical one-range addition theorems for STOs and Coulomb–Yukawa-like correlated interaction potentials (CIPs) with integer and noninteger indices. The final results are especially useful for the computations of arbitrary multicenter multielectron integrals that arise in the Hartree–Fock–Roothaan (HFR) approximation and also in the correlated methods based upon the use of STOs as basis functions.

COMPUTATION OF THREE-CENTER OVERLAP INTEGRALS OVER NONINTEGER n SLATER TYPE ORBITALS USING Ψα-ETO

Using complete orthonormal sets of Ψα-exponential type orbitals (Ψα- ETO , α = 1, 0, -1, -2,…), the three-center overlap integrals over noninteger n STO (NISTO) appearing in the evaluation of multicenter–multielectron integrals of central and noncentral interaction potentials are calculated. The final results are expressed in terms of one- or two-center overlap integrals between NISTO and integer n STO (ISTO). The formulas obtained are valid for arbitrary noninteger principal quantum numbers, screening parameters, and location of NSTO.

Unified Treatment for Two-Center One-Electron Molecular Integrals Over Slater Type Orbitals with Integer and Noninteger Principal Quantum Numbers

A unified expression has been obtained for two-center one-electron molecular integrals over Slater type orbitals with integer and noninteger principal quantum numbers by the use of the expansion formula for the product of two normalized associated Legendre functions. The presented expression for two-center one-electron molecular integrals contains the expansion coefficients akk' us and Mulliken integrals An and Bn. The efficiency of the presented calculation has been compared with that of other methods, indicating good convergence and great numerical stability for a wide range of quantum numbers, orbital exponents and internuclear distances

Unified treatment of overlap integrals with integer and noninteger n Slater-type orbitals using translational and rotational transformations for spherical harmonics

A unified treatment of two-center overlap integrals over Slater-type orbitals (STO) with integer and noninteger values of the principal quantum numbers is described. Using translation and rotation formulas for spherical harmonics, the overlap integrals with integer and noninteger n Slater-type orbitals are expressed through the basic overlap integrals and spherical harmonics. The basic overlap integrals are calculated using auxiliary functions Aσ and Bk. The analytical relations obtained in this work are especially useful for the calculation of overlap integrals for large integer and noninteger principal quantum numbers. The formulas established in this study for overlap integrals can be used for the construction of series expansions based on addition theorems. PACS Nos.: 31.15.–p, 31.20.Ej