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Time-dependent Density Functional Theory (TDDFT) has become successful for its balance of economy and accuracy. However, the application of TDDFT to large systems or long time scales remains computationally prohibitively expensive. In this paper, we investigate the numerical stability and accuracy of two subspace propagation methods to solve the time-dependent Kohn-Sham equations with finite and periodic boundary conditions. The bases considered are the Lanczos basis and the adiabatic eigenbasis. The results are compared to a benchmark fourth-order Taylor expansion of the time propagator. Our results show that it is possible to use larger time steps with the subspace methods, leading to computational speedups by a factor of 2–3 over Taylor propagation. Accuracy is found to be maintained for certain energy regimes and small time scales.

A complex potential is constructed to inject electrons into the conduction band, mimicking electron currents in nanoscale systems. The injected electrons are time propagated until a steady state is reached. The local current density can then be calculated to show the path of the conducting electrons on an atomistic level. The method allows for the calculation of the current density vectors within the medium as a function of energy of the conducting electron. Using this method, we investigate the electron pathway of graphene nanoribbons in various structures, molecular junctions, and black phosphorus nanoribbons. By analyzing the current flow through the structures, we find strong dependence on the structural geometry and the energy of the injected electrons. This method may be of general use in the study of nano-electronic materials and interfaces.A complex potential is constructed to inject electrons into the conduction band, mimicking electron currents in nanoscale systems. The injected electrons are time propagated until a steady state is reached. The local current density can then be calculated to show the path of the conducting electrons on an atomistic level. The method allows for the calculation of the current density vectors within the medium as a function of energy of the conducting electron. Using this method, we investigate the electron pathway of graphene nanoribbons in various structures, molecular junctions, and black phosphorus nanoribbons. By analyzing the current flow through the structures, we find strong dependence on the structural geometry and the energy of the injected electrons. This method may be of general use in the study of nano-electronic materials and interfaces.