Over the course of the past few decades, quantum mechanical calculations based on Kohn-Sham density functional theory (DFT) have become a cornerstone of materials, physical, and chemical sciences research by virtue of the predictive power and fundamental insights they provide. The widespread use of the methodology can be attributed to its generality, simplicity, and high accuracy-to-cost ratio relative to other such ab initio approaches. However, the solution of the Kohn-Sham equations remains a formidable task, scaling cubically with the number of atoms, therefore being restricted in the size and type of systems for which it can be used. 

1D nanostructures such as nanotubes, nanowires, and nanocoils have received  increased attention over the past three decades due to their exciting and fascinating properties. Indeed, such structures are not just limited to those synthesized, but are also commonly found in nature, e.g., DNA, viruses, and proteins. It is common for these 1D systems to possess non-translational symmetry, with cyclic and helical perhaps the most frequent. Even otherwise, the close association of bending and torsion with cyclic and helical symmetries, respectively, makes them ubiquitous. Since Kohn-Sham implementations employing systematically improvable discretizations work in affine coordinate systems, translational symmetry is readily incorporated. However, non-conventional symmetries like cyclic and/or helical are not compatible with affine coordinate systems, and therefore have not been incorporated/exploited. 

The research efforts in the current project include the following:

• A cyclic+helical symmetry-adapted formulation and large-scale parallel implementation of Kohn-Sham DFT has been developed. In particular, the structural and electronic symmetry of the system has been used to reduce all equations/computations to the fundamental domain, which enables the previously intractable ab initio characterization of nanostructures as well as their response to mechanical deformations. For instance, twisted nanotubes can require O(100, 000) atoms in the simulation domain when employing periodic boundary conditions, which reduces to O(3) atoms in the proposed method. 
• The tremendous simplification provided by the symmetry-adapted Kohn-Sham method has been used to study the (i) response of carbon nanotubes to torsional deformations in both the linear and nonlinear regime; (ii) bending moduli of forty-four select atomic monolayers; (iii) direction-dependent bending response of rectangular atomic monolayers, (iv) transversal flexoelectric coefficients --- electromechanical property that represents a two-way coupling between strain gradients and polarization, for which a novel formulation at large deformations has been developed --- for fifty-four select atomic monolayers; (v) elastic properties for forty-five transition metal dichalcogenide (TMD) nanotubes and twenty-seven Janus TMD nanotubes; (vi) and effect of deformations on the electronic properties for forty-five TMD nanotubes, eighteen Janus TMD nanotubes, and twelve transition metal dihalide (TMH) nanotubes. In all cases, regression models have been developed to aid in the understanding of the behavior/response.

Overall, the developed formalism has opened an avenue for understanding the interplay between mechanical, electronic, optical, and thermal effects at the nanoscale, where continuum theories lack the fidelity. It has also accelerated the design of systems with tailored properties.

The educational efforts of the project include 

• Interdisciplinary training of graduate students at the intersection of mechanics, mathematics, materials science, physics, and chemistry.
• Development of course materials for undergraduate as well as graduate courses. 
• Organization of multiple interdisciplinary symposiums at important research conferences.
• Broad dissemination of results through the PI's research group websites.

Last Modified: 10/30/2022
Modified by: Phanish Suryanarayana