The prediction of atomic kinetic energies from coordinates of surrounding atoms using kriging machine learning

Timothy L. Fletcher, Shaun M. Kandathil, Paul L A Popelier

    Research output: Contribution to journalArticlepeer-review


    A novel design of a next-generation force field considers not only the electronic inter-atomic energy but also intra-atomic energy. This strategy promises a faithful mapping between the force field and the quantum mechanics that underpins it. Quantum chemical topology provides an energy partitioning in which atoms have well-defined electronic kinetic energies, and we are interested in capturing how they respond to changes in the positions of surrounding atoms. A machine learning method called kriging successfully creates models from a training set of molecular configurations that can then be used to predict the atomic kinetic energies occurring in previously unseen molecular configurations. We present a proof-of-concept based on four molecules of increasing complexity (methanol, N-methylacetamide, glycine and triglycine). We test how well the atomic kinetic energies can be modelled with respect to training set size, molecule size and elemental composition. For all atoms tested, the mean atomic kinetic energy errors fall below 1.5 kJ mol-1, and far below this in most cases. This represents errors all under 0.5 % and thus the kinetic energies are well modelled using the kriging method, even when using modest-to-small training set sizes. © 2014 Springer-Verlag Berlin Heidelberg.
    Original languageEnglish
    Pages (from-to)1499-1459
    Number of pages9
    JournalTheoretical Chemistry Accounts
    Issue number7
    Publication statusPublished - 2014


    • Force field
    • Kinetic energy
    • Kriging
    • Quantum chemical topology (QCT)
    • Quantum theory of atoms in molecules (QTAIM)


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