30.2.1 The general ansatz

The conventional external pair functions are augmented by terms of the form

$$\vert u_{ijp}^{\rm F12}\rangle = \sum_{p=\pm 1} \sum_{kl} T^{ijp}_{kl} \hat Q_{12} \hat F_{12} \vert kl\rangle$$ (11)

This ansatz is orbital invariant (i.e., the same results are obtained with canonical or localized orbitals), but it often suffers from geminal basis set superposition errors. Furthermore, singularities may occur in the zeroth-order Hamiltonian, in particular for larger systems. Therefore, this ansatz is normally not recommended.