One-range Addition Theorems for Noninteger n Slater Functions using Complete Orthonormal Sets of Exponential Type Orbitals in Standard Convention

By the use of complete orthonormal sets of -exponential type orbitals ( -ETOs) with integer (for alpha (*) = alpha) and noninteger self-frictional quantum number alpha (*)(for alpha (*) not equal alpha) in standard convention introduced by the author, the one-range addition theorems for -noninteger n Slater type orbitals -NISTOs) are established. These orbitals are defined as follows psi((alpha))(nlm)(zeta,(r) over right arrow) = (2 zeta)(3/2)/Gamma(p(l)*+1) [Gamma(q(l)*+1)/(2n)(alpha)*(n-l-1)!](1/2) e(-x/2)x(1)(l)F(1)(-[n-l-1]; p(l)* + 1; x) S-lm(theta,phi) chi(n*lm)(zeta,(r) over right arrow) = (2 zeta)(3/2)[Gamma(2n*+1)](-1/2) x(n)*(-1)e(-x/2)S(lm)(theta,phi), where x = 2 zeta r, 0 < zeta < infinity, p(l)* = 2l + 2 - alpha*, q(l)* = n + l + 1 - alpha*, -infinity < alpha* < 3, -infinity < alpha <= 2, F-1(1) is the confluent hypergeometric function and are the complex or real spherical harmonics. The origin of the -ETOs, therefore, of the one-range addition theorems obtained in this work for -NISTOs is the self-frictional potential of the field produced by the particle itself. The obtained formulas can be useful especially in the electronic structure calculations of atoms, molecules and solids when Hartree-Fock-Roothan approximation is employed.