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We present an implementation of time-dependent density-functional theory (TDDFT) in the linear response formalism enabling the calculation of low energy optical absorption spectra for large molecules and nanostructures. The method avoids any explicit reference to canonical representations of either occupied or virtual Kohn-Sham states and thus achieves linear-scaling computational effort with system size. In contrast to conventional localised orbital formulations, where a single set of localised functions is used to span the occupied and unoccupied state manifold, we make use of two sets of in situ optimised localised orbitals, one for the occupied and one for the unoccupied space. This double representation approach avoids known problems of spanning the space of unoccupied Kohn-Sham states with a minimal set of localised orbitals optimised for the occupied space, while the in situ optimisation procedure allows for efficient calculations with a minimal number of functions. The method is applied to a number of medium sized organic molecules and a good agreement with traditional TDDFT methods is observed. Furthermore, linear scaling of computational cost with system size is demonstrated on a system of carbon nanotubes.
Linear-response time-dependent (TD) density-functional theory (DFT) has been implemented in the pseudopotential wavelet-based electronic structure program BigDFT and results are compared against those obtained with the all-electron Gaussian-type orbi
We demonstrate that Daubechies wavelets can be used to construct a minimal set of optimized localized contracted basis functions in which the Kohn-Sham orbitals can be represented with an arbitrarily high, controllable precision. Ground state energie
Time-Dependent Density Functional Theory (TDDFT) has recently been extended to describe many-body open quantum systems (OQS) evolving under non-unitary dynamics according to a quantum master equation. In the master equation approach, electronic excit
We analyze possible nonlinear exciton-exciton correlation effects in the optical response of semiconductors by using a time-dependent density-functional theory (TDDFT) approach. For this purpose, we derive the nonlinear (third-order) TDDFT equation f
Linear scaling methods for density-functional theory (DFT) simulations are formulated in terms of localised orbitals in real-space, rather than the delocalised eigenstates of conventional approaches. In local-orbital methods, relative to conventional