Brief review related to the foundations of time-dependent density functional theory

The electron density n(\rb,t), which is the central tool of time-dependent density functional theory, is presently considered to be derivable from a one-body time-dependent potential V(\rb,t), via one-electron wave functions satisfying a time- dependent Schr\"{o}dinger equation. This is here related via a generalized equation of motion to a Dirac density matrix now involving $t$. Linear response theory is then surveyed, with a special emphasis on the question of causality with respect to the density dependence of the potential. Extraction of V(\rb,t) for solvable models is also proposed

Higher harmonics and ac transport from time dependent density functional theory

We report on dynamical quantum transport simulations for realistic molecular devices based on an approximate formulation of time-dependent Density Functional Theory with open boundary conditions. The method allows for the computation of various properties of junctions that are driven by alternating bias voltages. Besides the ac conductance for hexene connected to gold leads via thiol anchoring groups, we also investigate higher harmonics in the current for a benzenedithiol device. Comparison to a classical quasi-static model reveals that quantum effects may become important already for small ac bias and that the full dynamical simulations exhibit a much lower number of higher harmonics. Current rectification is also briefly discussed.Comment: submitted to J. Comp. Elec. (special issue

Implementation and benchmark of a long-range corrected functional in the density functional based tight-binding method

Bridging the gap between first principles methods and empirical schemes, the density functional based tight-binding method (DFTB) has become a versatile tool in predictive atomistic simulations over the past years. One of the major restrictions of this method is the limitation to local or gradient corrected exchange-correlation functionals. This excludes the important class of hybrid or long-range corrected functionals, which are advantageous in thermochemistry, as well as in the computation of vibrational, photoelectron and optical spectra. The present work provides a detailed account of the implementation of DFTB for a long-range corrected functional in generalized Kohn-Sham theory. We apply the method to a set of organic molecules and compare ionization potentials and electron affinities with the original DFTB method and higher level theory. The new scheme cures the significant overpolarization in electric fields found for local DFTB, which parallels the functional dependence in first principles density functional theory (DFT). At the same time the computational savings with respect to full DFT calculations are not compromised as evidenced by numerical benchmark data

Effect of line defects on the electrical transport properties of monolayer MoS2_{2} sheet

We present a computational study on the impact of line defects on the electronic properties of monolayer MoS2. Four different kinds of line defects with Mo and S as the bridging atoms, consistent with recent theoretical and experimental observations are considered herein. We employ the density functional tight-binding (DFTB) method with a Slater-Koster type DFTB-CP2K basis set for evaluating the material properties of perfect and the various defective MoS2 sheets. The transmission spectra is computed with a DFTB-Non-Equilibrium Greens Function (NEGF) formalism. We also perform a detailed analysis of the carrier transmission pathways under a small bias and investigate the phase shifts in the transmission eigenstates of the defective MoS2 sheets. Our simulations show a 2-4 folds decrease in carrier conductance of MoS2 sheets in the presence of line defects as compared to that for the perfect sheet

Towards a simplified description of thermoelectric materials: Accuracy of approximate density functional theory for phonon dispersions

We calculate the phonon-dispersion relations of several two-dimensional materials and diamond using the density-functional based tight-binding approach (DFTB). Our goal is to verify if this numerically efficient method provides sufficiently accurate phonon frequencies and group velocities to compute reliable thermoelectric properties. To this end, the results are compared to available DFT results and experimental data. To quantify the accuracy for a given band, a descriptor is introduced that summarizes contributions to the lattice conductivity that are available already in the harmonic approximation. We find that the DFTB predictions depend strongly on the employed repulsive pair-potentials, which are an important prerequisite of this method. For carbon-based materials, accurate pair-potentials are identified and lead to errors of the descriptor that are of the same order as differences between different local and semi-local DFT approaches

Time-dependent versus static quantum transport simulations beyond linear response

To explore whether the density-functional theory non-equilibrium Green's function formalism (DFT-NEGF) provides a rigorous framework for quantum transport, we carried out time-dependent density functional theory (TDDFT) calculations of the transient current through two realistic molecular devices, a carbon chain and a benzenediol molecule inbetween two aluminum electrodes. The TDDFT simulations for the steady state current exactly reproduce the results of fully self-consistent DFT-NEGF calculations even beyond linear response. In contrast, sizable differences are found with respect to an equilibrium, non-self-consistent treatment which are related here to differences in the Kohn-Sham and fully interacting susceptibility of the device region. Moreover, earlier analytical conjectures on the equivalence of static and time-dependent approaches in the low bias regime are confirmed with high numerical precision.Comment: 4 pages, 4 figure

Charge-transfer excited states in phosphorescent organo-transition metal compounds: a difficult case for time dependent density functional theory?

Light emitting organo-transition metal complexes have found widespread use in the past. The computational modelling of such compounds is often based on time-dependent density functional theory (TDDFT), which enjoys popularity due to its numerical efficiency and simple black-box character. It is well known, however, that TDDFT notoriously underestimates energies of charge-transfer excited states which are prominent in phosphorescent metal–organic compounds. In this study, we investigate whether TDDFT is providing a reliable description of the electronic properties in these systems. To this end, we compute 0–0 triplet state energies for a series of 17 pseudo-square planar platinum(II) and pseudo-octahedral iridium(III) complexes that are known to feature quite different localization characteristics ranging from ligand-centered (LC) to metal-to-ligand charge transfer (MLCT) transitions. The calculations are performed with conventional semi-local and hybrid functionals as well as with optimally tuned range-separated functionals that were recently shown to overcome the charge transfer problem in TDDFT. We compare our results against low temperature experimental data and propose a criterion to classify excited states based on wave function localization. In addition, singlet absorption energies and singlet–triplet splittings are evaluated for a subset of the compounds and are also validated against experimental data. Our results indicate that for the investigated complexes charge-transfer is much less pronounced than previously believed

Phonon-induced band gap renormalization by dielectric dependent global hybrid density functional tight-binding

Accurate electronic bandstructures of solids are indispensable for a wide variety of applications and should provide a sound prediction of phonon-induced band gap renormalization at finite temperatures. We employ our previously introduced formalism of general hybrid functionals within the approximate density functional method, DFTB, to present first insights into the accuracy of temperature dependent band gaps obtained by a dielectric-dependent global hybrid functional. The work targets the prototypical group-IV semiconductors diamond and silicon. Following Zacharias et al. [Phys. Rev. Lett. 115, 177401 (2015)], we sample the nuclear wave function by stochastic Monte-Carlo integration as well as the deterministic one-shot procedure [Phys. Rev. B 94, 075125 (2016)] derived from it. The computational efficiency of DFTB enables us to further compare these approaches, which fully take nuclear quantum effects into account, with classical Born-Oppenheimer molecular dynamic (BOMD) simulations. While the quantum mechanical treatments of Zacharias et al. yield band gaps in good agreement with experiment, calculations based on BOMD snapshots inadequately describe the renormalization effect at low temperatures. We demonstrate the importance of properly incorporating nuclear quantum effects by adapting the stochastic approach to normal amplitudes that arise from the classical equipartition principle. For low temperatures the results thus obtained closely resemble the BOMD predictions, while anharmonic effects become important beyond $500\,\mathrm{K}$. Comparisons between DFTB parametrized from semi-local DFT, and global hybrid DFTB, suggest that Fock-type exchange systematically yields a slightly more pronounced electron-phonon interaction, hence stronger gap renormalization and zero-point corrections

Electron–phonon scattering in molecular electronics: from inelastic electron tunnelling spectroscopy to heating effects

In this paper, we investigate dissipation in molecular electronic devices. Dissipation is a crucial quantity which determines the stability and heating of the junction. Moreover, several experimental techniques which use inelastically scattered electrons as probes to investigate the geometry in the junction are becoming fundamental in the field. In order to describe such physical effects, a non-equilibrium Green's function (NEGF) method was implemented to include scattering events between electrons and molecular vibrations in current simulations. It is well known that the final heating of the molecule depends also on the ability of the molecule to relax vibrational quanta into the contact reservoirs. A semi-classical rate equation has been implemented and integrated within the NEGF formalism to include this relaxation. The model is based on two quantities: (i) the rate of emission of phonons in the junction by electron–phonon scattering and (ii) a microscopic approach for the computation of the phonon decay rate, accounting for the dynamical coupling between the vibrational modes localized on the molecule and the contact phonons. The method is applied to investigate inelastic electron tunnelling spectroscopy (IETS) signals in CO molecules on Cu(110) substrates as well as dissipation in C60 molecules on Cu(110) and Si(100) surfaces. It is found that the mechanisms of energy relaxation are highly mode-specific and depend crucially on the lead electronic structure and junction geometry

An efficient method for quantum transport simulations in the time domain

An approximate method based on adiabatic time dependent density functional theory (TDDFT) is presented, that allows for the description of the electron dynamics in nanoscale junctions under arbitrary time dependent external potentials. In this scheme, the density matrix of the device region is propagated according to the Liouville-von Neumann equation. The semi-infinite leads give rise to dissipative terms in the equation of motion which are calculated from first principles in the wide band limit. In contrast to earlier {\em ab-initio} implementations of this formalism, the Hamiltonian is here approximated by a density expansion in the spirit of the density functional based tight-binding (DFTB) method without introducing empirical parameters. Results are presented for two prototypical molecular devices and compared to calculations at the full TDDFT level. The issue of non-existence of a steady state under certain conditions is also briefly touched on