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Personne# Ksenia Briling

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Ksenia Briling, Alberto Fabrizio

Machine learning (ML) algorithms have undergone an explosive development impacting every aspect of computational chemistry. To obtain reliable predictions, one needs to maintain a proper balance between the black-box nature of ML frameworks and the physics of the target properties. One of the most appealing quantum-chemical properties for regression models is the electron density, and some of us recently proposed a transferable and scalable model based on the decomposition of the density onto an atom-centered basis set. The decomposition, as well as the training of the model, is at its core a minimization of some loss function, which can be arbitrarily chosen and may lead to results of different quality. Well-studied in the context of density fitting (DF), the impact of the metric on the performance of ML models has not been analyzed yet. In this work, we compare predictions obtained using the overlap and the Coulomb-repulsion metrics for both decomposition and training. As expected, the Coulomb metric used as both the DF and ML loss functions leads to the best results for the electrostatic potential and dipole moments. The origin of this difference lies in the fact that the model is not constrained to predict densities that integrate to the exact number of electrons N. Since an a posteriori correction for the number of electrons decreases the errors, we proposed a modification of the model, where N is included directly into the kernel function, which allowed lowering of the errors on the test and out-of-sample sets.

Ksenia Briling, Alberto Fabrizio, Sergio Vela Llausi

The ab initio determination of electronic excited state (ES) properties is the cornerstone of theoretical photochemistry. Yet, traditional ES methods become impractical when applied to fairly large molecules, or when used on thousands of systems. Machine learning (ML) techniques have demonstrated their accuracy at retrieving ES properties of large molecular databases at a reduced computational cost. For these applications, nonlinear algorithms tend to be specialized in targeting individual properties. Learning fundamental quantum objects potentially represents a more efficient, yet complex, alternative as a variety of molecular properties could be extracted through postprocessing. Herein, we report a general framework able to learn three fundamental objects: the hole and particle densities, as well as the transition density. We demonstrate the advantages of targeting those outputs and apply our predictions to obtain properties, including the state character and the exciton topological descriptors, for the two bands (n pi* and pi pi*) of 3427 azoheteroarene photoswitches.

Ksenia Briling, Alberto Fabrizio

Physics-inspired molecular representations are the cornerstone of similarity-based learning applied to solve chemical problems. Despite their conceptual and mathematical diversity, this class of descriptors shares a common underlying philosophy: they all rely on the molecular information that determines the form of the electronic Schrödinger equation. Existing representations take the most varied forms, from non-linear functions of atom types and positions to atom densities and potential, up to complex quantum chemical objects directly injected into the ML architecture. In this work, we present the spectrum of approximated Hamiltonian matrices (SPAHM) as an alternative pathway to construct quantum machine learning representations through leveraging the foundation of the electronic Schrödinger equation itself: the electronic Hamiltonian. As the Hamiltonian encodes all quantum chemical information at once, SPAHM representations not only distinguish different molecules and conformations, but also different spin, charge, and electronic states. As a proof of concept, we focus here on efficient SPAHM representations built from the eigenvalues of a hierarchy of well-established and readily-evaluated “guess” Hamiltonians. These SPAHM representations are particularly compact and efficient for kernel evaluation and their complexity is independent of the number of different atom types in the database.

2022