The core methodology employed in this work is based on the so-called incremental expansion, which allows to represent the PES as a mathematical series converging to the exact solution when written in its complete form or provide an approximate treatment of PES when truncated. It is common in the field to apply such truncated expansions to restrict direct mode-mode couplings when calculating approximate PESs. In my work, I demonstrated that methods of machine learning can effectively complement this approach and give an access to inexpensive and accurate evaluations of high-order expansion terms avoiding more costly quantum chemical calculations. As was shown previously, incremental expansions can also be applied to fragment the total molecule into smaller subsystems such that expensive calculations of the total system are avoided and only smaller fragments are considered. This results in the double incremental expansion of PES. Since in my work PESs are calculated at grid points, it was important to ensure that the employed grids are constructed automatically and that they are optimal, i.e. include as small number of points to be calculated as possible still accurately describing PESs. Such an automatic grid construction approach within the framework of doubly-incremental PES was successfully developed during this project and tested on chain-like molecules. Its further expansion with methods of machine learning is currently in progress. To ensure a high impact and dissemination, intermediate findings were presented at scientific conferences and meetings. End results were published in the high-ranked peer-review Journal of Chemical Physics and made available by means of the arXiv research data repository. The corresponding algorithms were implemented in the open-source MidasCpp program and are, therefore, freely available to the end user.
Even larger molecular systems can be targeted by combining the above-mentioned approaches with density embedding techniques, which describe large surrounding molecular environments by means of embedding potentials. Another advantage of these techniques is that they provide an easy route to calculations of diabatic PESs. In the current project, I investigated the performance of density embedding techniques for diabatization on molecular systems including up to 2000 atoms. These test calculations were compared versus experimental results and shown to be sufficiently accurate for molecular properties such as spin densities. Additional work (in progress) was carried out to further improve and generalize this method to multiple electronic states. End results of this project were published in the high-ranked peer-review Journal of Physical Chemistry B and uploaded to the ChemRxiv research data repository. The described methodology was made publicly available by implementing it in the open-source quantum chemistry Serenity program.
