Motivated by an experiment in which the singlet-triplet gap in triphenylene based copolymers was effectively tuned, we used time dependent density functional theory (TDDFT) to reproduce the main results. By means of conventional and long-range correc
ted exchange correlation functionals, the luminescence energies and the exciton localization were calculated for a triphenylene homopolymer and several different copolymers. The phosphorescence energy of the pure triphenylene chain is predicted accurately by means of the optimally tuned long-range corrected LC-PBE functional and slightly less accurate by the global hybrid B3LYP. However, the experimentally observed fixed phosphorescence energy could not be reproduced because the localization pattern is different to the expectations: Instead of localizing on the triphenylene moiety - which is present in all types of polymers - the triplet state localizes on the different bridging units in the TDDFT calculations. This leads to different triplet emission energies for each type of polymer. Yet, there are clear indications that long-range corrected TDDFT has the potential to predict the triplet emission energies as well as the localization behavior more accurate than conventional local or semi-local functionals.
The time-dependent density functional based tight-binding (TD-DFTB) approach is generalized to account for fractional occupations. In addition, an on-site correction leads to marked qualitative and quantitative improvements over the original method.
Especially, the known failure of TD-DFTB for the description of sigma -> pi* and n -> pi* excitations is overcome. Benchmark calculations on a large set of organic molecules also indicate a better description of triplet states. The accuracy of the revised TD-DFTB method is found to be similar to first principles TD-DFT calculations at a highly reduced computational cost. As a side issue, we also discuss the generalization of the TD-DFTB method to spin-polarized systems. In contrast to an earlier study [Trani et al., JCTC 7 3304 (2011)], we obtain a formalism that is fully consistent with the use of local exchange-correlation functionals in the ground state DFTB method.
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.
Using the shift-operator technique, a compact formula for the Fourier transform of a product of two Slater-type orbitals located on different atomic centers is derived. The result is valid for arbitrary quantum numbers and was found to be numerically
stable for a wide range of geometrical parameters and momenta. Details of the implementation are presented together with benchmark data for representative integrals. We also discuss the assets and drawbacks of alternative algorithms available and analyze the numerical efficiency of the new scheme.
Holas, Howard and March [Phys. Lett. A {bf 310}, 451 (2003)] have obtained analytic solutions for ground-state properties of a whole family of two-electron spin-compensated harmonically confined model atoms whose different members are characterized b
y a specific interparticle potential energy u($r_{12}$). Here, we make a start on the dynamic generalization of the harmonic external potential, the motivation being the serious criticism levelled recently against the foundations of time-dependent density-functional theory (e.g. [J. Schirmer and A. Dreuw, Phys. Rev. A {bf 75}, 022513 (2007)]). In this context, we derive a simplified expression for the time-dependent electron density for arbitrary interparticle interaction, which is fully determined by an one-dimensional non-interacting Hamiltonian. Moreover, a closed solution for the momentum space density in the Moshinsky model is obtained.
