FAIMP is an ab initio rigorous way to introduce the electrostatic interactions and Pauli repulsion between the metal and the environment, however, perhaps not surprisingly, it has shown poor performance in the accurate modelling of the electronic structure of Ln(III) complexes 13 . To improve on this model, while keep pursuing a fragment ab initio approach to describe the metalligand interactions essentially in terms of intermolecular forces, let us start again from eq.( ), fix the sets of spin-orbitals {f R i } for all groups to some optimal orbitals obtained for the isolated fragments, and, crucially, relax the strong-orthogonality constraints.