HartreeFock
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Compute gradient, Hessian matrix
The derivatives could be computed numerically (central difference would be my choice). In fact, they could be computed 'analytically', but I don't think I would use that method for this project, I suppose the post-HF things would complicate things even more.
They could be used for optimizations computations, that is, computation of molecular structure. Also vibrational modes & frequencies could be computed. Ideally, also the lines intensity...