Construction of Different Kinds of Atomic and Molecular Orbitals Using Complete Orthonormal Sets of Ψ^α-ETO in Single Exponent Approximation

Using complete orthonormal sets of Ψ^α-exponential type orbitals in single exponent approximation the new approach has been suggested for construction of different kinds of functions which can be useful in the theory of linear combination of atomic orbitals. These functions can be chosen properly according to the nature of the problems under consideration. This is rather important because the choice of the basis set may be play a crucial role in applications to atomic and molecular problems. As an example of application, different atomic orbitals for the ground states of the neutral and the first ten cationic members of the isoelectronic series of He atom are constructed by the solution of Hartree--Fock--Roothaan equations using Ψ¹, Ψ⁰ and Ψ^-1 basis sets. The calculated results are close to the numerical Hartree-Fock values. The total energy, expansion coefficients, orbital exponents and virial ratio for each atom are presented.