What is it about?

Machine learning rapidly infiltrated many areas of chemical research, enabling targeted design of new molecules and materials and assisting in the development of new simulation techniques. For a machine to learn chemical properties, it needs to know the structure and composition of a chemical system. This information is provided by molecular representations, which convert chemical compounds into machine-readable numerical arrays, graphs, text strings, etc. However, many popular chemical representations face two critical limitations. Firstly, they cannot distinguish between molecules with identical or similar geometries but different charges and spin multiplicities. In other words, such representations fall short of describing, for instance, the species involved in the charge transport through organic semiconductors, such as those found in our smartphone screens. Secondly, they cannot encode the so-called periodic systems – a term that captures everything from the aforementioned organic semiconductors to the bulk of water in a glass or the graphite rod in a pencil. Our representation entitled matrix of orthogonalised atomic orbital coefficients (MAOC) eliminates both of these bottlenecks. MAOC is based on a cost-effective localisation scheme that represents localised orbitals via a predefined set of atomic orbitals. The latter can be constructed from small atom-centred basis sets in conjunction with a guess electronic configuration of the molecule.

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Why is it important?

Several aspects of MAOC make it unique compared to other geometry- and Hamiltonian-based representations: MAOC can encode not only molecules, but also atoms and periodic systems, and can distinguish compounds with identical compositions and geometries but distinct charges and spin multiplicities. Moreover, MAOC can be used to analyse how the electronic structure governs the properties in a chemically intuitive manner.


Open-shell compounds, such as radical ions of N-heteropolycycles, are central to my PhD research. I quickly realised that even though there are many ways to represent neutral closed-shell compounds, charged open-shell forms are harder to handle because they require quantum mechanics to incorporate charge and spin multiplicity. MAOC, being a change and spin variant orbital-based representation, solves this problem.

Stiv Llenga
Heidelberger Institut fur Theoretische Studien

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This page is a summary of: Matrix of orthogonalized atomic orbital coefficients representation for radicals and ions, The Journal of Chemical Physics, June 2023, American Institute of Physics, DOI: 10.1063/5.0151122.
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