We present recent results of the time-dependent density functional based tight-binding method (TD-DFTB). The scheme is characterized by (i) the use of a limited, usually minimal basis, (ii) a two-center approximation for the Kohn-Sham Hamiltonian, (iii) a second-order functional expansion of the total energy and (iv) the simplification of two-electron integrals in the Mulliken approximation. The range of validity of these approximations is assessed by comparison to first principles time-dependent density functional theory (TDDFT) calculations in converged basis sets. The approach is free of empirical parameters and can be used to evaluate optical spectra for systems with several hundred atoms.

To illustrate typical applications of the method, we show results for so-called nanohoops. More precisely termed [n]Cycloparaphenylenes ([n]CPPs), these are fascinating molecules due to their high molecular symmetry, and have only recently been successfully synthesized. They can be regarded as the smallest possible single-walled carbon nanotube (SWCNT), and have fueled speculations of their use as template to synthesize armchair (n,n) SWCNTs from the bottom up. They are also of great interest in their own right for materials sciences due to their photophysical properties, most notably an unusual blueshift of UV/Vis emission wavelength with increasing size n.

Besides the linear response TD-DFTB treatment in the frequency domain, if time allows, we also discuss direct propagation in the time domain leading to an O(N) scheme and an implementation for open boundary conditions, suitable for applications in molecular electronics.

Salle de séminaire IRSAMC, Jeudi 11 Janvier, 14h - 15h