Machine learning (ML) models are increasingly used in combination with electronic structure calculations to predict molecular properties at a much lower computational cost in highthroughput settings. Such ML models require representations that encode the molecular structure, which are generally designed to respect the symmetries and invariances of the target property. However, size-extensivity is usually not guaranteed for so-called global representations. In this contribution, we show how extensivity can be built into global ML models using, e. g., the Many-Body Tensor Representation. Properties of extensive and non-extensive models for the atomization energy are systematically explored by training on small molecules and testing on small, medium and large molecules. Our results show that non-extensive models are only useful in the size-range of their training set, whereas extensive models provide reasonable predictions across large size differences. Remaining sources of error for extensive models are discussed.
A metal-organic polyhedral network with a unique 5-connected topology is expanded into a series using different metal ions or dicarboxylate ligands. The prototype material (ZmID), [Zn(4)(mip)(4)(dabco)(OH(2))(2)] (mip = 5-methylisophthalate, dabco = diazabicyclo[2.2.2]octane), is based on 5-connecting paddlewheel motifs and possesses large cage-like pores (8-20 A diameter). The metal ion is replaced by Co(2+) and/or the dicarboxylate by isophthalate (ip) or 2,7-naphthalenedicarboxylate (2,7-ndc) to give isoreticular frameworks [Zn(4)(ip)(4)(dabco)(OH(2))(2)] (ZID), [Co(4)(ip)(4)(dabco)(OH(2))(2)] (CID), and [Zn(4)(2,7-ndc)(4)(dabco)(OH(2))(2)] (ZND). X-ray powder diffraction and gas sorption studies reveal that ZID and CID have sustainable pore structures and show higher N(2) uptakes than ZmID. ZND is found unstable with respect to the removal of guest solvents. ZmID, ZID, and CID are all similar in terms of the H(2) sorption capacities (1.4-1.5 wt % at 77 K and 1 bar) and isosteric heat of H(2) adsorption (6-7 kJ/mol at low coverage).
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