  We present a combination of the incremental expansion of potential energy
surfaces (PESs), known as n-mode expansion, with the incremental evaluation of
the electronic energy in a many-body approach. The application of semi-local
coordinates in this context allows the generation of PESs in a very
cost-efficient way. For this, we employ the recently introduced flexible
adaptation of local coordinates of nuclei (FALCON) coordinates. By introducing
an additional transformation step, concerning only a fraction of the
vibrational degrees of freedom, we can achieve linear scaling of the
accumulated cost of the single point calculations required in the PES
generation. Numerical examples of these double incremental approaches for
oligo-phenyl examples show fast convergence with respect to the maximum number
of simultaneously treated fragments and only a modest error introduced by the
additional transformation step. The approach, presented here, represents a
major step towards the applicability of vibrational wave function methods to
sizable, covalently bound systems.
