Spatial Prediction of Electronic Wavefunctions from Reciprocal Lattices: Visualization of Electronic Properties of 2D Materials Using Deep Convolutional Neural Networks

The representation of electronic wavefunctions in real space grids, which are directly related to molecular orbitals and electronic densities either in molecular or crystalline systems, is a fundamental part of many studies at ab initio levels, since it contributes to the understanding of complex physical and chemical phenomena at the nanoscale. This work proposes the use of a deep convolutional neural network for the prediction of electronic wavefunctions at arbitrary positions along high-symmetry points within the reciprocal space (first Brillouin zone), which can be represented as isosurfaces in the real space. The proposed neural network algorithm is trained with data from density functional theory (DFT) calculations of monolayer 2D crystalline systems (i.e., pristine, B- and N-doped graphene, and MoS2) and was able to produce predictions of data for wavefunction representation on the real space, with accuracies in between 62% and 92%, from calculated determination coefficients. Moreover, the optimized method for generating spatial representations of electronic wavefunctions, based on Machine Learning, is at least 25× faster than the conventional DFT-based methodology, enabling an efficient way for a quick assessment of 2D material properties related to the spatial distribution of electronic wavefunctions in the real space, such as local charge density and molecular orbital visualization in crystalline systems, and including their dependence on the position within the reciprocal space.