We present a systematic procedure to generate a compact basis for molecular computations made of atomic orbitals and their derivatives with respect to the total electronic charge. All electron density functional computations for small molecules highlight the rapid convergence to the basis set limit. The simplicity of the basis set construction allows a fine tuning with respect to the electronic structure method (Hartree-Fock, configuration interaction, density functional, etc.), resulting in improved performance and in reduced basis set superposition errors. We discuss the connection of our scheme with chemical concepts like Fukui functions or absolute hardness and the relation with the linearized methods (linear augmented plane waves, linear muffin tin orbitals) of solid state physics.