Accurate many-body repulsive potentials for density-functional tight binding from deep tensor neural networks

Machine learning (ML) has been proven to be an extremely valuable tool for simulations with ab initio accuracy at the computational cost between classical interatomic potentials and density-functional approximations. Similar efficiency can only be achieved by semi-empirical methods, such as density-functional tight-binding (DFTB). One of the limiting factors in terms of the accuracy and transferability of DFTB parametrizations is the so-called repulsive potential, which plays a considerable role for the prediction of energetic, structural, and dynamical properties. Few attempts of using ML-techniques to address this issue have been proposed recently but, up to now, evidence of transferability and scalability is still scarce. Hence, we combine DFTB with deep tensor neural networks (DTNN) to maximize the strengths of both approaches. The DTNN is used to construct a non-linear model for the localized many-body interatomic repulsive energy, substantially improving upon standard DFTB and DTNN. The resulting DFTB+DTNN model yields accurate predictions of several physicochemical properties for a large variety of organic molecules compared to the hybrid DFT-PBE0 functional. DFTB+DTNN thus opens a route to the fast access to reliable property calculation of diverse molecular systems.