Robust fitting techniques in the chain of spheres approximation to the Fock exchange: The role of the complementary space.

The chain of spheres seminumerical integration algorithm is reexamined from the point of view of various numerical error cancellation schemes. The two sources of ideas are the robust fitting technique of Dunlap and the dealiasing concept of the pseudospectral methods of Friesner. The most efficient scheme is identified and is found to be a generalization of the overlap fitting procedure discussed earlier. It will be shown that due to the conceptual similarity between complementary auxiliary basis functions of explicitly correlated approaches and the dealiasing functions of pseudospectral methods, the former can be used in a similar manner as the latter to cancel numerical errors. In contrast to the dealiasing functions, the complementary auxiliary basis functions are not specific to the integration grid. The scheme obtained can dramatically improve reaction energies even using small grid setups at a moderate additional cost.