Accurate prediction of the energetics of weakly bound complexes using the machine learning method kriging

Peter I Maxwell,Paul L A Popelier

doi:10.1007/s11224-017-0928-9

Abstract

Here, we extend the system energy prediction approach used in the force field FFLUX (Maxwell et al. Theor Chem Acc 135:195, 2016) to complexes bound by weak intermolecular interactions. The investigation features the first application of the approach to bound complex systems, additionally challenged by investigating complexes held together only weakly, through either a predominant dispersion contribution, or through mixed dispersion and hydrogen-bonding. Our approach uses the interacting quantum atoms (IQA) energy partitioning scheme to obtain the intra-atomic, {E}_{mathrm{intra}}^{mathrm{A}} , and interatomic, {V}_{mathrm{inter}}^{{mathrm{AA}}^{hbox{'}}} , energies, which when summed, compose the molecular energy, {E}_{mathrm{IQA}}^{mathrm{system}} . The {E}_{mathrm{intra}}^{mathrm{A}} and {V}_{mathrm{inter}}^{{mathrm{AA}}^{hbox{'}}} energies are mapped to the positions of the nuclear coordinates through the machine learning method kriging to build atomic energy models. A model’s quality is established through its ability to accurately predict the atomic and molecular energies of atoms in an external test set. Mean absolute error percentages (MAE%) of 1.5, 1.5, 1.6, 1.0, 2.6 and 1.7% are obtained in recovering the molecular energy for ammonia…benzene, water…benzene, HCN…benzene, methane…benzene, stacked-benzene (C2h) dimer and T-benzene (C2v) dimer complexes, respectively.

Highlights

Within a protein, one may expect to find several different types of interatomic interactions such as hydrogen bonds, halogen bonds, π-π stacking interactions and ionic bonds
At the heart of FFLUX are topological atoms defined by the Quantum Theory of Atoms in Molecules (QTAIM) [3,4,5,6]
FFLUX is such a force field: it is aware of the internal energy of an atom, as well as its various interaction energies, an atom’s charge, dipole moment and higher multipole moments

Summary

Introduction

One may expect to find several different types of interatomic interactions such as hydrogen bonds, halogen bonds, π-π stacking interactions and ionic bonds. The selected [12] machine learning method is Kriging [13], which has been tested successfully on a variety of systems, including ethanol [14], (peptide-capped) alanine [15], the microhydrated sodium ion [15], N-methylacetamide (NMA) and histidine [16], the four aromatic (peptidecapped) amino acids [17], all naturally occurring amino acids [18], helical deca-alanines [19, 20], water clusters [21], cholesterol [22] and carbohydrates [23] This collective work shows an existing proof-of-concept that kriging models generate sufficiently accurate atomic property models, and they do this directly from the coordinates of the surrounding atoms. The stackedbenzene (C2h) dimer involves a π-π stacking interaction, and the methane...benzene complex involves a C-H/π bond, common in protein side chains [31]

Methodology

Results

N test

40 T BENZENE

Compliance with ethical standards

Conclusions and further work