Recently we proposed a class of molecular representations for machine learning (ML) — Spectrum of approximated Hamiltonian matrices (SPA^HM) [1] based on lightweight one-electron Hamiltonians, widely used as an SCF initial guess in computational chemistry. SPA^HM naturally contains the information about the nuclear charges and positions as well as obeys the symmetries required for an effective ML representation.

The first variant is a compact global representation consisting of occupied-orbital eigenvalues of the approximated Hamiltonian. Owing to a seamless generalization to open-shell systems, SPA^HM performs well on datasets characterized by a wide variation of charge and spin, for which the traditional structure-based representations commonly fail.

Using our first eigenvalue-variant as a starting point, we then focus on designing local and transferable representations, through exploiting the occupied eigenvectors and associated density matrix. Bridging the advantages of both the SOAP [2] and SLATM [3], we construct similarity measures from density-based fingerprints expanded into atoms and bond contributions. The atomic (a) or bond (b) density overlap kernel is defined as a dot product of power spectra, which themselves are used as representation vectors [SPA^HM(a) and SPA^HM(b)] of an atomic environment.

Preliminary results indicate that the SPA^HM(a) is already competing with SLATM [3] for predicting atomic properties. Current efforts are placed into leveraging SPA^HM(a,b) to describe charged species, open-shell systems and properties derived from them.

[1] Alberto Fabrizio, Ksenia R. Briling, Clemence Corminboeuf, Digital Discovery, 2022, Advance Article (doi:10.1039/D1DD00050K).
[2] Albert P. Bartók, Risi Kondor, Gábor Csányi, Physical Review B, 2013, 87, 184115.
[3] Bing Huang, O. Anatole von Lilienfeld, Nature Chemistry, 2020, 12, 945–951.