SPA^HM(a,b): Encoding the Density Information from Guess Hamiltonian in Quantum Machine Learning Representations

Abstract

Recently, we introduced a class of molecular representations for kernel-based regression methods�the spectrum of approximated Hamiltonian matrices (SPA H M)�that takes advantage of lightweight one-electron Hamiltonians traditionally used as a self-consistent field initial guess. The original SPA H M variant is built from occupied-orbital energies (i.e., eigenvalues) and naturally contains all of the information about nuclear charges, atomic positions, and symmetry requirements. Its advantages were demonstrated on data sets featuring a wide variation of charge and spin, for which traditional structure-based representations commonly fail. SPA H M(a,b), as introduced here, expand the eigenvalue SPA H M into local and transferable representations. They rely upon one-electron density matrices to build fingerprints from atomic and bond density overlap contributions inspired from preceding state-of-the-art representations. The performance and efficiency of SPA H M(a,b) is assessed on the predictions for data sets of prototypical organic molecules (QM7) of different charges and azoheteroarene dyes in an excited state. Overall, both SPA H M(a) and SPA H M(b) outperform state-of-the-art representations on difficult prediction tasks such as the atomic properties of charged open-shell species and of π-conjugated systems.

Energetic Information from Information-Theoretic Approach in Density Functional Theory as Quantitative Measures of Physicochemical Properties

“…These energetic information quantities lend us more tools to understand and describe molecular properties. Besides, since these quantities are all well-defined universal density functionals, they provide additional descriptors that can be employed as robust features to establish more generally applicable models in machine learning and artificial intelligence in the future. − …”

3DReact: Geometric Deep Learning for Chemical Reactions

“…Physics-inspired representations that take as input the three-dimensional structure − (as well as, in some cases, electronic structure − ) of molecules and transform it into a fixed-length vector, while respecting known physical laws, have a rich history in molecular property prediction. − ,,,− Common desiderata − for high-performing representations are (i) smoothness, (ii) encoding of the appropriate symmetries to permutations, rotations and translations, , (iii) completeness and (iv) additivity to allow for extrapolation to larger systems. Such fingerprints, − ,− , being rooted in fundamental principles, are designed to be property-independent: a single representation can be constructed for a molecule to predict any quantum-chemical target.…”