  We show how to construct a linearly independent set of antisymmetrized
geminal power (AGP) states, which allows us to rewrite our recently introduced
geminal replacement models as linear combinations of non-orthogonal AGPs. This
greatly simplifies the evaluation of matrix elements and permits us to
introduce an AGP-based selective configuration interaction method, which can
reach arbitrary excitation levels relative to a reference AGP, balancing
accuracy and cost as we see fit.
