Investigation of atomic properties using orbitals with noninteger principal quantum numbers in hartree-fock-roothaan theory

In this study, properties of some multi-electron atoms, like the ground state energy, orbital energy and virial ratio, have been calculated on the suggested new equations of Hartree-Fock-Roothaan theory using new basis functions constructed from hyperbolic cosine and generalized exponential type orbitals with noninteger principal quantum numbers.This thesis is divided into two parts. In the first part, the formulae of suggested new equations in Hartree-Fock-Roothaan theory were obtained. Using these formulae, the general programs for Hartree-Fock-Roothaan equations were written for the closed and open shell atoms. Electronic properties of atoms have been calculated by the use of these programs. In these calculations, the relationship between optimized parameters of basis functions with noninteger principal quantum numbers and atomic number was investigated.In the second part of work, by examining the basis functions available in literature, two new more efficient basis functions are proposed. The results of total energy calculation have been obtained for atoms and compared with results of similar basis functions. The equations have been solved analytically using new basis functions and the efficiencies of these functions in atomic calculations were examined by comparing the similar works in literature.One of the most important problems in the determination of atomic properties is determination of the optimum parameters. On the basis of minimum total energy requirement, the optimum parameters in the basis functions used have been obtained by employing the optimization process.Usefulness of new equations in Hartree-Fock-Roothaan theory were demonstrated and efficiency of proposed basis functions have been determined by comparing the results obtained from this work and literature.