Adaptive Finite Element Approximations for Kohn-Sham Models

The Kohn-Sham equation is a powerful, widely used approach for computation of ground state electronic energies and densities in chemistry, materials science, biology, and nanosciences. In this paper, we study the adaptive finite element approximations for the Kohn-Sham model. Based on the residual type a posteriori error estimators proposed in this paper, we introduce an adaptive finite element algorithm with a quite general marking strategy and prove the convergence of the adaptive finite element approximations. Using D{\" o}rfler's marking strategy, we then get the convergence rate and quasi-optimal complexity. We also carry out several typical numerical experiments that not only support our theory,but also show the robustness and efficiency of the adaptive finite element computations in electronic structure calculations.Comment: 38pages, 7figure

Self-regulation mechanism for charged point defects in hybrid halide perovskites

Hybrid halide perovskites such as methylammonium lead iodide (CH3NH3PbI3) exhibit unusually low free carrier concentrations despite being processed at low-temperatures from solution. We demonstrate, through quantum mechanical calculations, that the origin of this phenomenon is a prevalence of ionic over electronic disorder in stoichiometric materials. Schottky defect formation provides a mechanism to self-regulate the concentration of charge carriers through ionic compensation of charged point defects. The equilibrium charged vacancy concentration is predicted to exceed 0.4% at room temperature. This behaviour, which goes against established defect conventions for inorganic semiconductors, has implications for photovoltaic performance

Prediction of Silicon-Based Layered Structures for Optoelectronic Applications

A method based on the particle swarm optimization (PSO) algorithm is presented to design quasi-two-dimensional (Q2D) materials. With this development, various single-layer and bi-layer materials in C, Si, Ge, Sn, and Pb were predicted. A new Si bi-layer structure is found to have a much-favored energy than the previously widely accepted configuration. Both single-layer and bi-layer Si materials have small band gaps, limiting their usages in optoelectronic applications. Hydrogenation has therefore been used to tune the electronic and optical properties of Si layers. We discover two hydrogenated materials of layered Si8H2 and Si6H2 possessing quasi-direct band gaps of 0.75 eV and 1.59 eV, respectively. Their potential applications for light emitting diode and photovoltaics are proposed and discussed. Our study opened up the possibility of hydrogenated Si layered materials as next-generation optoelectronic devices.Comment: 21 pages,6 figures, 1 tabe

Transferable E(3) equivariant parameterization for Hamiltonian of molecules and solids

Using the message-passing mechanism in machine learning (ML) instead of self-consistent iterations to directly build the mapping from structures to electronic Hamiltonian matrices will greatly improve the efficiency of density functional theory (DFT) calculations. In this work, we proposed a general analytic Hamiltonian representation in an E(3) equivariant framework, which can fit the ab initio Hamiltonian of molecules and solids by a complete data-driven method and are equivariant under rotation, space inversion, and time reversal operations. Our model reached state-of-the-art precision in the benchmark test and accurately predicted the electronic Hamiltonian matrices and related properties of various periodic and aperiodic systems, showing high transferability and generalization ability. This framework provides a general transferable model that can be used to accelerate the electronic structure calculations on different large systems with the same network weights trained on small structures.Comment: 33 pages, 6 figure