Use of ?? basis functions in the study of molecular electronic structure

In this study, the complete orthonormal sets of ?? (?=2,1,0,-1,... ) functions have been used as basis functions in Hartree-Fock-Roothaan method and their efficiency in the electronic structure calculations has been investigated. This thesis is divided into three parts. In the first part of the study, the efficiency of ?? basis functions in atomic energy calculations has been determined investigating some closed and open shell atoms with Z?36. In the second part, the multicenter integrals appearing in the molecular electronic structure calculations have been evaluated. The analytical formulas have been obtained for two-center one-electron integrals, Coulomb and Hybrid integrals by the use of ellipsoidal coordinates. One-range addition theorems have been used for the evaluation of two-center exchange, three and four center molecular integrals. Using derived formulas, the calculation results are in good agreement with the values obtained in literature for the arbitrary quantum numbers, screening constants and location of orbitals. In the third part, total electronic energies and linear combination coefficients to construct the wave functions have been found for BH, HF, N2 and H2O molecules performing the Hartree-Fock-Roothaan calculations.In the atomic and molecular energy calculations, minimal and double zeta basis sets have been used. According to the calculation results, the most efficient ?? basis functions have been found in the case of ?=2. The results obtained with ?2 functions have been discussed comparing to those obtained from other exponential type orbitals available in the literature.