Linear response excitations

In this chapter we will go through a couple of recipes for the computation of excited state properties using linear response time-dependent DFTB (TD-DFTB).

We can employ TD-DFTB to efficiently calculate vertical and adiabatic excitation energies, as well as the oscillator strengths of individual transitions. With this information, it is possible to compute the absorption spectra of a given system for a defined energy range. Furthermore, other properties like charges and energy gradients can be computed for specific excited states.

With DFTB+, we can investigate excited state properties of both closed- and open-shell molecular compounds. As DFTB+ is currently limited to finite systems only, the study of periodic structures has to be worked around by using properly optimised cluster models. As an instance of the latter case, we will examine below a recipe for the computation of the optical spectra of a titania-based cluster system.

Moreover, DFTB+ allows to speed up linear response calculations by reducing the dimension of the eigenvalue problem. This can be done for certain systems without incurring on a significant loss of accuracy, as will be shown in our macromolecule recipe.

Next, we will give a very brief introduction to linear response TD-DFTB. Feel free to skip this section if you are familiar with the theory. Afterwards, recipes for some diatomic molecules will be provided, covering different ground state multiplicity cases. We will then examine more complex systems, where the real power and efficiency of TD-DFTB will be exploited.

• Introduction
• Excitation energies of diatomic molecules
• Absorption spectrum of a macromolecule
• Absorption spectrum of NO-TiO2 complex
• Calculations using range-separated TD-DFTB
• Geometry relaxation in the excited state
• Visualization of natural orbitals with waveplot