Efficient determination of the Hamiltonian and electronic properties using graph neural network with complete local coordinates

Abstract Despite the successes of machine learning methods in physical sciences, prediction Hamiltonian, and thus electronic properties, is still unsatisfactory. Based on graph neural network (NN) architecture, we present an extendable NN model to determine Hamiltonian from ab initio data, with only local atomic structures as inputs. The rotational equivariance achieved by our complete coordinates (LCs). LC information, encoded using a convolutional designed preserve Hermitian symmetry, used map hopping parameters onto structures. We demonstrate performance graphene SiGe random alloys examples. show that model, although trained small-size systems, can predict well properties such band densities states for large-size systems within accuracy, justifying its extensibility. In combination high efficiency which takes seconds get 1728-atom system, work provides general framework efficiently accurately, new insights into computational physics will accelerate research large-scale materials.