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The progress of nanotechnology has led to the development of nanometer scale devices such as nano-antennas, molecular junctions, and others. The calculation of such devices' electromagnetic response becomes a challenge as it requires the integration of the classical form of Maxwell's equations with the quantum equations governing the electronic structure. To that end, Time-Dependent Density Functional Theory (TDDFT) reliably predicts the optical and electronic properties of molecules in the presence of external fields. However, most TDDFT formalisms only account for the electrostatic scalar potential, ignoring the presence of induced magnetic fields, and the retardation effects which follow. Disregarding the vector potential leads to an incorrect characterization of electronic structures exceeding certain size-to-wavelength ratio, the wavelength being that of the external electromagnetic field. In this work, the inclusion of induced vector potentials in the time-dependent Kohn-Sham equation is explored in both the Coulomb and Lorentz gauges. Although the Coulomb gauge is the commonly adapted gauge-fixing condition in TDDFT, the Lorentz gauge is shown to be just as effective in characterizing the response of electronic structures, bypassing the need for a projection scheme of the current density, via Helmholtz decomposition. In both gauges, fully incorporating the scalar and vector potentials can be computationally costly due to the retardation effects. Specifically, direct evaluation of the retarded integrals with their intrinsic dependence on past densities creates a computational bottleneck. To overcome this difficulty, highly efficient FFT-based integral methods utilizing multilevel schemes are employed. Carbon systems reaching the nanometric regime are explored in both gauges and various properties, appearing as a consequence of the newly incorporated induced fields, are demonstrated.

A fast evaluation of retarded electromagnetic potentials is presented for quantum calculations on a uniform Cartesian grid. The induced potentials are incorporated into the quantum Hamiltonian of the time-dependent density functional theory (TDDFT) in real space. Both Lorentz and Coulomb gauge-fixed Hamiltonians are implemented using a real-time propagation scheme. The efficiency of the resulting formalism and implementation enables the evaluation of retardation effects on long carbon chains.

Hybrid functionals combine Density Functional Theory (DFT) with a fraction of Fock exchange. Screened hybrid functionals use a screened Fock exchange instead. In recent years, those methods became more popular as they yield results that are in better agreement with experiment for various physical properties. However, the calculation of Fock exchange can be computationally intensive for large systems. In this paper, we demonstrate the use of an efficient real-space approach that is based on projection schemes and an FFT based Poisson solver, for large atomistic systems. We apply this approach for silicon quantum dots and graphene nanoribbons and show the size dependence of physical properties such as the band gap and ionization potential. Finally, we show how those calculations can be further accelerated through the use of Graphical Processing Units (GPUs).

We analyze with Density Functional Theory (DFT) calculations the adsorption of fluorine atoms on graphene. We show that the adsorbed atoms clustering is favored by energy considerations and show that there are long range patterns for the second atoms adsorption energy at different sites. Finally, we discuss the effect of the different adsorption patterns on the Fermi level shift and band structure distortion.

Concept of edge polarizability produced by support of the edge quantum states is demonstrated by the example of graphene nanoribbon with zigzag edge configuration. This concept allows to formulate physically correct edge conditions for electromagnetic field in nanostructures instead of ordinary Meixner conditions in classical electrodynamics.

The calculation of Fock-Exchange integral is becoming an important computational challenge in solving the quantum properties of systems with many electrons. In this work we show how techniques that are used in electromagnetic simulations for the similar Poisson equation can help in accelerating the calculation of such exchange integrals. The approach we present can be especially efficient for quasi-planar systems such as Graphene nano-ribbons (GNRs) or elongated systems such as carbon nano-tubes (CNTS) and the 1D Carbyne.