Local Potentials Reconstructed within Linearly Independent Product Basis Sets of Increasing Size.

Given a matrix representation of a local potential v ( r ) within a one-electron basis set of functions that form linearly independent products (LIP), it is possible to construct a well-defined local potential v ~ ( r ) that is equivalent to v ( r ) within that basis set and has the form of an expansion in basis function products. Recently, we showed that for exchange-correlation potentials v XC ( r ) defined on the infinite-dimensional Hilbert space, the potentials v ~ XC ( r ) reconstructed from matrices of v XC ( r ) within minimal LIP basis sets of occupied Kohn-Sham orbitals bear only qualitative resemblance to the originals. Here, we show that if the LIP basis set is enlarged by including low-lying virtual Kohn-Sham orbitals, the agreement between v ~ XC ( r ) and v XC ( r ) improves to the extent that the basis function products are appropriate as a basis for v XC ( r ). These findings validate the LIP technology as a rigorous potential reconstruction method.