An Iterative Technique for Solving the N -electron Hamiltonian: The Hartree-Fock method

The problem of electron motion in an arbitrary field of nuclei is an important quantum mechanical problem finding applications in many diverse fields. From the variational principle we derive a procedure, called the Hartree-Fock (HF) approximation, to obtain the many-particle wavefunction describing such a system. Here, the central physical concept is that of electron indistinguishability: while the antisymmetry requirement greatly complexifies our task, it also offers a symmetry that we can exploit. After obtaining the HF equations, we then formulate the procedure in a way suited for practical implementation on a computer by introducing a set of spatial basis functions. An example implementation is provided, allowing for calculations on the simplest heteronuclear structure: the helium hydride ion. We conclude with a discussion of deriving physical information from the HF solution.