1: Why are the elements of a basis set taken to be orthogonal? But in real sense atomic orbitals do overlap.
i realize that. i wasn't referring to the computation time required in solving the electronic structure of heavy metals, but rather the complications with regards to basis set and not getting a garbage answer.The number of basis functions involved in heavy atom electronic structure calculations are small compared to those needed for proteins. The smallest known protein has about 45 residues, and a couple of hundred atoms. This results in thousands of basis functions.
Now if you add a transition metal or two, then you've really got a lot. Not only do you have to compute a lot of integrals, but you have to form and diagonalize the Fock matrix or something like it.
Post-HF treatments are needed, in any case, for reliable results, and that's really out there for these systems.