Inclusion of More Physics Leads to Less Data: Learning the Interaction Energy as a Function of Electron Deformation Density with Limited Training Data

Abstract

Machine learning (ML) approaches to predicting quantum mechanical (QM) properties have made great strides toward achieving the computational chemist's holy grail of structure-based property prediction. In contrast to direct ML methods, which encode a molecule with only structural information, in this work, we show that QM descriptors improve ML predictions of dimer interaction energy, both in terms of accuracy and data efficiency, by incorporating electronic information into the descriptor. We present the electron deformation density interaction energy machine learning (EDDIE-ML) model, which predicts the interaction energy as a function of Hartree−Fock electron deformation density. We compare its performance with leading direct ML schemes and modern DFT methods for the prediction of interaction energies for dimers of varying charge type, size, and intermolecular separation. Under a low-data regime, EDDIE-ML outperforms other direct ML schemes and is the only model readily transferrable to larger, more complex systems including base pair trimers and porous cages. The underlying physical connection between the density and interaction energy enables EDDIE-ML to reach an accuracy comparable to modern DFT functionals in fewer training data points compared to other ML methods.

Electrostatic Embedding of Machine Learning Potentials

“…Therefore, this work is another example of how physics-based models with correct asymptotic behaviour can dramatically reduce the amount of data and free parameters required to achieve satisfactory predictive power of a model. 15,32 The Slater valence shells of MBIS partitioning approximately represent the typical decay of the electronic density and thus result in meaningful description of the electrostatic potential, despite it's simplicity. The QEq model captures the impact of all the chemical groups, even distant ones, on how the charge is distributed over the molecule.…”

Accurate Prediction of Three-Body Intermolecular Interactions via Electron Deformation Density-Based Machine Learning

“…The descriptor used in EDDIE-ML was originally formulated for predicting interaction energy curves for dimer systems. The electron deformation density Δρ for a dimer A ··· B , defined as Δρ AB = ρ AB – ρ A – ρ B , was found in conjunction with a GPR model to differentiate accurately between dimer systems separated by increasing intermolecular distance, within 0.3 kcal mol –1 for neutral monomers . Briefly, the descriptor formulation involves projection of the electron deformation density Δρ onto atom-centered basis functions, ψ n l m ( r⃗ ) = Y l m ( θ , φ ) ζ n ( r ) where Y l m (θ,φ) are spherical harmonics and ζ n ( r ) are radial basis functions with a cutoff radius of r 0 : , ζ̃ n ( r ) = { lefttrue 1 N r 2 false( r 0 − r false) n + 2 for r < r 0 0 else …”

“…GPR is a powerful interpolation method which has been widely used in the chemical machine learning community for predicting properties of materials and molecules. − Here, we follow the methodology developed in our earlier work to train a GPR model to predict interaction energies, while introducing a new hybrid kernel function to better resolve between atomic and molecular environments.…”

“…Recently, as an alternative to performing expensive interaction energy calculations at a highly correlated level of theory, we proposed a machine learning (ML) scheme based on the Hartree–Fock electron deformation density . This method belongs to the class of delta machine learning (Δ-ML) approaches, which has emerged in the past several years as a popular subclass of quantum ML methods which use the energy (or other property; in our case it is the electron density) calculated at a low level of theory such as Hartree–Fock (HF) or semilocal DFT to predict a more accurate value that is comparable to that calculated using a more expensive level of theory, but without the additional computational cost. − One of the greatest advantages of this approach is its data efficiency, with Δ-ML offering a middle ground between conventional direct ML models which require large volumes of training data to reach a given accuracy, and rigorous ab initio computation at highly correlated levels of theory.…”

Informing geometric deep learning with electronic interactions to accelerate quantum chemistry

“…A key bottleneck hampering the broader applicability of QM-informed approaches is the presence of unique many-body symmetries necessitated by an explicit treatment on electron-electron interactions. Heuristic schemes have been used to enforce invariance (24,26,(30)(31)(32)(33) at a potential loss of information in their input features or expressivity in their ML models. Two objectives remain elusive for QM-informed ML: 1) incorporate the underlying physical symmetries with maximal data efficiency and model flexibility and 2) accurately infer downstream molecular properties for large chemical spaces at a computational resource requirement on par with existing empirical and Atomistic ML methods.…”