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

Recently, we introduced a class of molecular representations for kernel-based regression methods─the spectrum of approximated Hamiltonian matrices (SPA^HM)─that takes advantage of lightweight one-electron Hamiltonians traditionally used as a self-consistent field initial guess. The original SPA^HM 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^HM(a,b), as introduced here, expand the eigenvalue SPA^HM 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^HM(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^HM(a) and SPA^HM(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.