From theory to computing: the Hartree–Fock model

The implementation of a Hartree–Fock computer program is addressed. A powerful method for the solution of the Hartree–Fock equations, developed by Roothaan and Hall and based on the expansion of the orbitals in a basis of known functions converts the Hartree–Fock problem into an algebraic one consisting in the diagonalization of a matrix. The organization of the workflow for the self-consistent field (SCF) procedure in a computer program implementing the Roothaan–Hall equations is discussed. Finally, the choice of an appropriate set of basis functions for the orbital expansion is discussed, with a focus on the so-called Cartesian Gaussian-type orbitals.