SPA$^\mathrm{H}$M(a,b): encoding the density information from guess Hamiltonian in quantum machine learning representations

TL;DR

This paper introduces SPA$^ ext{H}$M(a,b), novel molecular representations based on Hamiltonian eigenvalues and density matrices, which improve prediction accuracy for complex charged and excited-state molecules in quantum machine learning.

Contribution

The paper extends SPA$^ ext{H}$M to local and transferable forms using density matrices, enhancing performance on challenging molecular datasets.

Findings

SPA$^ ext{H}$M(a,b) outperform existing representations on charged and excited molecules.

The new methods are efficient and transferable across different molecular systems.

They achieve superior accuracy in predicting atomic properties of complex molecules.

Abstract

Recently, we introduced a class of molecular representations for kernel-based regression methods -- the spectrum of approximated Hamiltonian matrices (SPA$^\mathrm{H}$M) -- that takes advantage of lightweight one-electron Hamiltonians traditionally used as an SCF initial guess. The original SPA$^\mathrm{H}$M variant is built from occupied-orbital energies (ie, eigenvalues) and naturally contains all the information about nuclear charges, atomic positions, and symmetry requirements. Its advantages were demonstrated on datasets featuring a wide variation of charge and spin, for which traditional structure-based representations commonly fail. SPA$^\mathrm{H}$M(a,b), as introduced here, expand the eigenvalue SPA$^\mathrm{H}$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$^\mathrm{H}$M(a,b) is assessed on the predictions for datasets of prototypical organic molecules (QM7) of different charges and azoheteroarene dyes in an excited state. Overall, both SPA$^\mathrm{H}$M(a) and SPA$^\mathrm{H}$M(b) outperform state-of-the-art representations on difficult prediction tasks such as the atomic properties of charged open-shell species and of $\pi$-conjugated systems.