  Following the recent demonstration that van der Waals forces control the
ferroelectric ordering of layers within nanoflakes and bulk samples of
CuBiP2Se6 and CuInP2S6, it is demonstrated that they also control the internal
geometrical structure of isolated monolayers of these materials. This internal
structure involves large displacements of the copper atoms, either normal to
the layer plane or else within the plane, that change its ligation environment.
In both cases, the van der Waals dispersion force out-competes traditional
bonding effects to control structure. However, we find that the aspects of the
dispersion force giving rise to each effect are uncorrelated: long range
effects control inter-layer ferroelectric ordering whereas short-range effects
control internal layer structure. These conclusions are drawn considering
predicted properties of monolayers, bilayers, and bulk materials obtained using
14 density-functional-theory based methods. While the different methods used
often predict starkly different quantitative results, they concur as to the
basic nature of ABP2X6 materials. Of the methods used, only the PBE-D3 and
optPBEvdW methods were found to predict a wide range of observed properties
without serious disparity. Finding optimal computational methods remains a
significant challenge for which the unusual multi-scale nature of the van der
Waals interactions in ABP2X6 materials provides demanding criteria.
