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Two types of approaches to modeling molecular systems have demonstrated high practical efficiency. Density functional theory (DFT), the most widely used quantum chemical method, is a physical approach predicting energies and electron densities of molecules. Recently, numerous papers on machine learning (ML) of molecular properties have also been published. ML models greatly outperform DFT in terms of computational costs, and may even reach comparable accuracy, but they are missing physicality - a direct link to Quantum Physics - which limits their applicability. Here, we propose an approach that combines the strong sides of DFT and ML, namely, physicality and low computational cost. By generalizing the famous Hohenberg-Kohn theorems, we derive general equations for exact electron densities and energies that can naturally guide applications of ML in Quantum Chemistry. Based on these equations, we build a deep neural network that can compute electron densities and energies of a wide range of organic molecules not only much faster, but also closer to exact physical values than curre
Machine learning models are poised to make a transformative impact on chemical sciences by dramatically accelerating computational algorithms and amplifying insights available from computational chemistry methods. However, achieving this requires a c
The applications of machine learning techniques to chemistry and materials science become more numerous by the day. The main challenge is to devise representations of atomic systems that are at the same time complete and concise, so as to reduce the
Statistical learning algorithms are finding more and more applications in science and technology. Atomic-scale modeling is no exception, with machine learning becoming commonplace as a tool to predict energy, forces and properties of molecules and co
The concept of machine learning configuration interaction (MLCI) [J. Chem. Theory Comput. 2018, 14, 5739], where an artificial neural network (ANN) learns on the fly to select important configurations, is further developed so that accurate ab initio
Quantum scattering calculations for all but low-dimensional systems at low energies must rely on approximations. All approximations introduce errors. The impact of these errors is often difficult to assess because they depend on the Hamiltonian param