A method for the generation of atomic basis sets adapted to the presence of the external time-dependent electric field perturbation is presented. The resulting basis sets with explicit dependence on the oscillatory perturbation are then used to develop a method for the immediate generation of highly compact sets of polarization functions. The very high computational efficiency of the approach proposed in this Letter is illustrated by calculations of the dynamic polarizability of the He atom in a very wide range of frequencies. (C) 2004 Elsevier B.V. All rights reserved.