When we think of chemical bonding, we usually think only of the valence orbitals. It is these orbitals that form bonds, and the core orbitals are not involved in the chemistry. To be sure, this is only a qualitative picture, but it raises the question of whether we really need to consider the core orbitals in our calculations. For heavy elements, the number of core orbitals is not small. An element such as platinum, from the third transition series, has 30 orbitals in the first four shells that could be classed as core orbitals. If these remain essentially atomic over some region of the molecular potential energy surface, they might as well be fixed in their atomic form. That is, we would make a frozen-core approximation, and all that the core orbitals are doing is supplying a nonlocal static potential that could be evaluated once and used for the remainder of the calculation. As relativistic effects are to a large extent localized in the core region, they could be included in the frozen-core potential. We could then treat the valence orbitals and the orbitals on the light atoms nonrelativistically, as we did in the previous chapter. This would save all the work of calculating the relativistic integrals, and the calculation would be as cheap as a nonrelativistic calculation. There is one main difficulty with this idea, and that is the orthogonality of the rest of the orbitals to the frozen core. The basis sets we use in molecular calculations are not automatically orthogonal to the core of any one atom: we must make them so by some procedure, such as Schmidt orthogonalization. But this involves taking linear combinations of the core and valence orbitals, and then we not only have to calculate all the integrals involving the core, we also have to transform them to the orthogonal basis. The reintroduction of the core integrals means that we have to calculate all the relativistic contributions that we had previously put into the frozen-core potential. Obviously, this is not a satisfactory state of affairs. Two solutions to this problem are in common use.