Machine learning based prediction of the electronic structure of quasi-one-dimensional materials under strain

We present a machine learning based model that can predict the electronic structure of quasi-one-dimensional materials while they are subjected to deformation modes such as torsion and extension/compression. The technique described here applies to important classes of materials systems such as nanotubes, nanoribbons, nanowires, miscellaneous chiral structures, and nanoassemblies, for all of which, tuning the interplay of mechanical deformations and electronic fields, i.e., strain engineering, is an active area of investigation in the literature. Our model incorporates global structural symmetries and atomic relaxation effects, benefits from the use of helical coordinates to specify the electronic fields, and makes use of a specialized data generation process that solves the symmetry-adapted equations of Kohn-Sham density functional theory in these coordinates. Using armchair single-wall carbon nanotubes as a prototypical example, we demonstrate the use of the model to predict the fields associated with the ground-state electron density and the nuclear pseudocharges, when three parameters (namely, the radius of the nanotube, its axial stretch, and the twist per unit length) are specified as inputs. Other electronic properties of interest, including the ground-state electronic free energy, can be evaluated from these predicted fields with low-overhead postprocessing, typically to chemical accuracy. Additionally, we show how the nuclear coordinates can be reliably determined from the predicted pseudocharge field using a clustering-based technique. Remarkably, only about 120 data points are found to be enough to predict the three-dimensional electronic fields accurately, which we ascribe to the constraints imposed by symmetry in the problem setup, the use of low-discrepancy sequences for sampling, and efficient representation of the intrinsic low-dimensional features of the electronic fields. We comment on the interpretability of our machine learning model and anticipate that our framework will find utility in the automated discovery of low-dimensional materials, as well as the multiscale modeling of such systems