Mixed Basis Sets for Atomic Calculations

Many numerical methods of atomic calculations use one-electron basis sets. These basis sets must meet rather contradictory requirements. On the one hand, they must include physically justified orbitals, such as Dirac-Fock ones, for the one-electron states with high occupation numbers. On the other hand, they must ensure rapid convergence of the calculations in respect to the size of the basis set. It is difficult to meet these requirements using a single set of orbitals, while merging different subsets may lead to linear dependence and other problems. We suggest a simple unitary operator that allows such merging without aforementioned complications. We demonstrated robustness of the method on the examples of Fr and Au.