Overlap Integrals

The first type of integrals required in quantum chemical calculations are overlap integrals. These measure the overlap between atomic basis functions used in the calculation. Their importance is directly obvious: since we build molecular orbitals from atomic orbitals, it is important to quantify the degree of linear dependency of the basis of atomic orbitals.

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When solving the Hartree-Fock equations, a generalised secular problem is obtained. This can be rotated into a matrix diagonalization problem by basis set orthogonalisation. The most commonly used method to build an orthogonal basis set is the method of Loewdin or symmetric orthogonalization, though in principle any other method could be employed.

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