Accurate TDDFT absorption spectra over full spectral range

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Time dependent density functional theory (TDDFT) has proven to be a reliable work horse for obtaining absorption spectra and other related excited state quantities. Yet, calculation of entire absorption spectra can be very demanding and their evaluation is computationally prohibited for large system sizes. Roughly speaking TDDFT can be divided in two regimes, the linear-response or frequency domain time dependent density functional theory (LR-TDDFT) and in real-time time dependent density functional theory (RT-TDDFT). In the latter the time dependent Kohn-Sham states are explicitly propagated in time under the influence of a time dependent external potential. However, a large number of time steps is usually required to obtain the required accuracy and calculations for large systems becomes quickly unfeasible. LR-TDDFT aims to solve a non-hermitian eigenvalue problem in order to obtain the excited states. Generally speaking, the number of such excited states grows with system size and solving the linear algebra problem becomes also computational prohibited for large systems. Within the project we will develop a new approach for calculating full TDDFT spectra where the computational cost should not dramatically exceed the cost of the underlying ground state calculation. In particular we will obtain reliable approximated entire TDDFT spectra in combination with hybrid functional DFT. Thus our target is to provide accurate absorption spectra over a large spectral range and for large system sizes. For this purpose we suggest a method which combines the strengths of LR-TDDFT and RT-TDDFT to overcome the current limitations in system size. In order to reduce the computational cost to a minimum we aim at using very short time propagation in RT-TDDFT. As the resolution of the spectra significantly depends on the simulation time one can expect that this works already quite well for a spectrum which is characterized by a continuum or quasi continuum of states. However, it will fail if the spectrum also includes discrete excitations as the simulation time might be too short to achieve the desired resolution. Missing information about discrete excitations can be included using LR-TDDFT. Solving the eigenvalue problem associated with the linear-response formalism gives distinct excitation energies in form of eigenvalues of the particular problem. To keep the computational cost at a minimum we will approximately solve the LR equations using the so called small matrix approximation (SMA). The SMA will serve as a basis for more sophisticated approximations which will allow high accuracy in describing certain excitations or certain spectral regions. By this we envision an approach which guarantees the fast evaluation of entire TDDFT spectra in combination with high accuracy.