Exercise Week 12: TDDFT

This week’s exercise is about the theoretical aspects of ultraviolet-visible spectroscopy, usually abbreviated as UV/Vis. This sounds fairly similar to infrared spectroscopy, but it is not. The physical processes behind absorption in the ultraviolet-visible and infrared spectral ranges are totally different: The absorption of infrared light by a molecule typically leads to the excitation of nuclear vibrations, while the electronic system remains in its ground state. The absorption of (higher energy) ultraviolet-visible photons on the other hand leads to excitations of the electrons themselves. The principal difference between infrared and UV/Vis spectroscopy is therefore not the spectral range in which it happens, but whether the nuclear system or the electronic system is excited!

Nowadays the by far the most popular method for the calculation of electronically excited states is time-dependent density functional theory (TD-DFT). The name is not exactly a great choice as for the end user of the method there is absolutely no time anywhere in his calculation. However, the methods name is due to the fact that its derivation is based on calculating electron density’s linear response to a small time-dependent perturbation in the external potential, which models the electric field of the electromagnetic wave that is light.

The idea behind the TDDFT is that instead of describing an electronically excited state by a single orbital transition, TD-DFT describes a linear combination of multiple single orbital transitions. For example, an excitation which is mostly HOMO → LUMO, but also mixes some other single orbital transitions with larger orbital energy differences, such as HOMO → LUMO+1 and HOMO−1 → LUMO, etc.

TDDFT, just like other theoretical spectroscopy theories, is not about how photon interacts with electrons or phonons. That is what quantum field theory concerns. We only care about the energies. In order for a photon to be absorbed, its energy has to match with the excitation energy of one of the excited states of the molecule. However, not all excited states can be reached by absorption of photon and some exitations are more likely to be triggered by an incoming photon (of the correct energy) than others. In other words: For the prediction of an absorption spectrum, we not only need the position of the absorption bands (aka the excitation energies) but also their intensities.

In this exercise we will simulate the excitation energies and their intensities of acetone (CH₃)₂CO using CP2K. Here is the input example.

N.B. If you use our LSTS group’s computatonal nodes to do the calculation, please run module load intel/64Bit/2017v4 before using CP2K.

The key information in this CP2K input example is the TDDFPT section. It defines the TDDFT related settings. The COORD section is left empty.