Constructing realistic tight-binding models via differentiable programming

Differentiable programming(DP) is a programming paradigm of evaluating derivatives by applying automatic differentiation, which can handle a large scale of parameters. With its high efficiency and accuracy, DP has been widely used in machine learning and other gradient-based optimization(GBO) problems. In this letter, we implement DP in constructing realistic tight-binding(TB) models that usually have a large number of parameters. By fitting the band structure from the first-principles calculation, building a realistic TB model can be transformed into a GBO problem. We first analyzed the computation graph and demonstrated that the time complexity of DP is O(N) which is much smaller than O(N²) in the conventional finite differentiation, where N is the number of parameters. Then, we further explicitly demonstrate the power of our new method to build the TB model for silicon with around 7*10⁴ parameters, which cannot be accomplished with finite differentiation. Moreover, other physics constraints in building TB models, such as symmetry requirements, can be attached to the GBO process due to the great flexibility and compatibility of DP. Our work provides an efficient and accurate method to construct realistic TB models suitable for large-scale simulations of real materials.