Machine learning molecular conformational energies using semi-local density fingerprints

With the potential to sidestep the steep cost associated with high-level quantum-chemical calculations, machine learning (ML) has become an increasingly more viable approach in the field of theoretical and computational chemistry/physics over the past decade. In this work, we describe a novel molecular descriptor that goes beyond structural data and incorporates the wealth of information contained in semi-local descriptors of the electron density (i.e., ρ(r) and ▽ρ(r))—the quantum-mechanical objects at the very heart of density functional theory (DFT). The proposed “semi-local density fingerprint” (SLDF) molecular descriptor transforms the most energetically-relevant information in ρ(r) into a unique and compact (system-size-independent) representation for each molecule. By construction, SLDFs are global molecular descriptors that are atomic-species independent, invariant to translations, rotations, and permutations, and account for molecular symmetry. In a series of proof-of-principle tests, we demonstrate that SLDF-based ML models are able to predict molecular conformational energies and complex potential energy surfaces with high fidelity, even when the training does not include the test molecule.