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.