The electronic Schrödinger equation describes the motion of electrons under Coulomb interaction forces in the field of clamped nuclei and forms the basis of quantum chemistry. The talk is first concerned with the regularity properties of the corresponding wavefunctions that are compatible with the Pauli principle. It is shown that these solutions possess certain square integrable mixed weak derivatives of order up to N+1 with N the number of electrons. The result mathematically substantiates approximation methods that are based on the idea of sparse grids or hyperbolic cross spaces. A construction of this type is presented.