Ground State Energy Calculations of Isoelectronic Series of He in Double-Zeta Approximation Using Coulomb Potential with Noninteger Indices

Abstract

Using formulae for one- and two-electron integrals of Coulomb interaction potential fk(r) = r−k with non-integer indices k established by one of the authors with the help of complete orthonormal sets of Ψα-exponential-type orbitals (α = 1, 0, -1, -2, …), we perform the calculations for isoelectronic series of the He atom containing nuclear charges from 2 to 10, where k = 1 - μ (-1 < μ < 0). For this purpose we have used the double-zeta approximation, the configuration interaction and coupled-cluster methods employing the integer-n Slater-type orbitals as basis sets. It is demonstrated that the results of calculations obtained are better than the numerical Hartree–Fock values.