Here’s a little project that I’ve been meaning to finish for awhile now, to aid my own learning and anybody else who is interested: it’s a Maple script for a restricted closed-shell Hartree Fock program, which you can download here. (To open, right-click the link, save it locally, and then open with Maple – else you just get a bunch of XML) I wrote it using Maple 16, so it should work in v16 or later.
At the moment, it uses an SCF procedure to solve a simple HeH+ wave function in a basis set of contracted Gaussian functions. It includes detailed comments, and follows closely the text on p 106 – 176 of the book ‘Modern Quantum Chemistry’ (MQC) by Szabo & Ostlund. This Maple script could easily be extended to larger molecular systems, but the time required to calculate the two-electron integrals will mean that you’ll spend a lot of time staring at your computer screen! Incidentally, it turns out that Maple 16’s standard integrate command is pretty speedy for evaluating the overlap & kinetic energy integrals. For two-electron and nuclear repulsion integrals, it’s not so good! So I’ve used the analytical formulas in Appendix A of MQC.