The theory and implementation of different Hartree-Fock SCF methods have been discussed in this thesis. Methods to solve the Hartree-Fock equations for large molecules have also been discussed. For instance, the ideas behind the direct SCF, semi-direct SCF and density-matrix based SCF have been presented. The traditional Hartree-Fock SCF method has been coded and used for solving the Hartree-Fock equations for test cases. Numerical finite-element methods to calculate one and two-electron interaction integrals are also described. A finite-element based method to calculate kinetic energy integrals have been developed and implemented in a computer program using the Fortran 2003 language. The correctness and accuracy of the calculated integrals were checked by solving the Schrödinger and the Hartree-Fock equations for the three-dimensional harmonic oscillator and hydrogen molecule, respectively.
