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The accurate representation of multidimensional potential energy surfaces isa necessary requirement for realistic computer simulations of molecularsystems. The continued increase in computer power accompanied by advances incorrelated electronic structure methods nowadays enable routine calculations ofaccurate interaction energies for small systems, which can then be used asreferences for the development of analytical potential energy functions (PEFs)rigorously derived from many-body expansions. Building on the accuracy of theMB-pol many-body PEF, we investigate here the performance of permutationallyinvariant polynomials, neural networks, and Gaussian approximation potentialsin representing water two-body and three-body interaction energies, denotingthe resulting potentials PIP-MB-pol, BPNN-MB-pol, and GAP-MB-pol, respectively.Our analysis shows that all three analytical representations exhibit similarlevels of accuracy in reproducing both two-body and three-body reference dataas well as interaction energies of small water clusters obtained fromcalculations carried out at the coupled cluster level of theory, the currentgold standard for chemical accuracy. These results demonstrate the synergybetween interatomic potentials formulated in terms of a many-body expansion,such as MB-pol, that are physically sound and transferable, andmachine-learning techniques that provide a flexible framework to approximatethe short-range interaction energy terms.

journal of chemical physics online/the journal of chemical physics/journal of chemical physics

Comparison of permutationally invariant polynomials, neural networks,  and Gaussian approximation potentials in representing water interactions  through many-body expansions