Many-Body Descriptors for Predicting Molecular Properties with Machine Learning: Analysis of Pairwise and Three-Body Interactions in Molecules

Abstract

Machine learning (ML) based prediction of molecular properties across chemical compound space is an important and alternative approach to efficiently estimate the solutions of highly complex many-electron problems in chemistry and physics. Statistical methods represent molecules as descriptors that should encode molecular symmetries and interactions between atoms. Many such descriptors have been proposed; all of them have advantages and limitations. Here, we propose a set of general two-body and three-body interaction descriptors which are invariant to translation, rotation, and atomic indexing. By adapting the successfully used kernel ridge regression methods of machine learning, we evaluate our descriptors on predicting several properties of small organic molecules calculated using density-functional theory. We use two data sets. The GDB-7 set contains 6868 molecules with up to 7 heavy atoms of type CNO. The GDB-9 set is composed of 131722 molecules with up to 9 heavy atoms containing CNO. When trained on 5000 random molecules, our best model achieves an accuracy of 0.8 kcal/mol (on the remaining 1868 molecules of GDB-7) and 1.5 kcal/mol (on the remaining 126722 molecules of GDB-9) respectively. Applying a linear regression model on our novel many-body descriptors performs almost equal to a nonlinear kernelized model. Linear models are readily interpretable: a feature importance ranking measure helps to obtain qualitative and quantitative insights on the importance of two- and three-body molecular interactions for predicting molecular properties computed with quantum-mechanical methods.

Data‐Driven Materials Science: Status, Challenges, and Perspectives

“…Such structural descriptors have been successfully applied in the prediction of molecular and crystalline properties, [203,205,229] and there their development has exploded in recent years. [202,203,205,[229][230][231][232][233][234][235][236][237][238] To facilitate easier navigation through descriptor choices, application-neutral software libraries for descriptors are being developed. [239,240] In contrast to human-driven feature engineering, the optimal features can also be discovered more systematically by learning them directly from the data with feature learning.…”

From DFT to machine learning: recent approaches to materials science–a review

“…We now present a relatively chronological list used in recent materials research, which is considerable but not exhaustive. These include: bondorientational order parameters (BOP) [243]; Behler-Parrinello atom-centered symmetry functions (ACSF) [233,244], and its modified [245] and weighted (wACSF) [246] versions; Gaussian Approximation Potentials (GAP) [212,232] using smooth overlap of atomic positions (SOAP) [213] also extended for tensorial properties [247]; Coulomb matrix [248] and Bag of Bonds (BOB) [249], and the subsequent interatomic many body expansions (MBE) [250,251] like the so-called BAML (bonds, angles machine learning) [252] and fixed-size inverse distances [253]; metric fingerprints [238]; bispectrum [213]; atomic local frame (ALF) [254]; partial radial and angular distribution functions (PRDF, ADF) [255] and generalized radial distribution functions (GRDF) [224]; Fourier series of radial distribution functions [256]; force vectors representations [257]; spectral neighbor analysis potential (SNAP) [258]; permutation invariant polynomials [245]; particle densities [259]; angular Fourier series (AFS) [213]; topological polyhedra [260], Voronoi [261] and Voronoi-Dirichlet [262] tessellations; spherical harmonics [263]; histogram of distances, angles, or dihedral angles [264]; classical forcefield-inspired descriptors (CFID) [209]; graph-based such as Graph Approximated Energy (GRAPE) [265]; constant complexity descriptors based on Chebyshev polynomials [266]; symmetrized gradient-domain machine learning ...…”

“…Roughly two classes of properties can be predicted, or classified, using machine learning methods: bandgaps and electronic conductivity. The former being widely explored by regression techniques, capable of presenting a numerical value for the gap [206,210,253,264,[452][453][454][455][456][457][458][459][460][461][462], or classification methods, which simply provide an answer to the question 'is this compound or material a metal?' [463].…”

Quantum-Chemical Insights from Interpretable Atomistic Neural Networks

“…Due to the repeated interaction corrections, spatial information is propagated across multiple atoms. Thus, many-body interactions can be inferred without having to explicitly include angular or higher-order information [16,41,42].…”