4. Semi-empirical and empirical methods

When solving the HF-Roothaan equations, one of the most time-consuming steps is the calculation of the (rs|pq)-bi-electronic integrals entering the expression of the matrix elements of the Fock matrix F defined by the relation (24) . If n is the dimension of the basis, the number of bi-electronic integrals amounts to n ⁴ , which limits the size of the molecules studied. At a time when computing resources were very limited, quantochemists tried to imagine a simplification of these calculations, which would enable any molecular system to be treated without size restrictions. The introduction of approximations into the HF-Roothaan...