To calculate the excited state properties and processes of semiconductors (e.g. during the photocatalysis process), can be important. Non-Adiabatic Molecular Dynamics (NAMD) is one of the popular methods. I think NAMD still works within the DFT framework according to the introduction of the PYXAID Program and Hefei-NAMD.
But since the DFT works not so well when dealing with semiconductors and excited-state calculations, wouldn't NAMD be too erroneous considering the nuclei vibrations?
"But since the DFT works not so well when dealing with semiconductors and excited-state calculations, wouldn't NAMD be too erroneous considering the nuclei vibrations?"
First of all, DFT in this context might not be as bad as you think. For example, my answer to: What are some recent developments in density functional theory? shows that even 10 years ago in 2011, some functionals were on average within 1.8 kcal/mol of CCSD(T) for a study across 30 test sets involving 1218 total energies overall. The double-hybrids described there, were extended for application to excited states within the TDDFT framework as early as in 2007 with this paper.
Still, in many applications 1 kcal/mol is not accurate enough, but in such applications, the entire NAMD framework might not be either. In the PDF presentation about Hefei-NAMD which you showed us in your question body, search for the word "assumptions" and you will see that Hefei-NAMD is far from an "exact" method for dynamics predictions in general. Likewise in the PDF paper about the PYXAID program which again you showed us in your question body, just search for the word "neglected" and "approximate" and you'll find corners that are being cut in that program, which will prevent you from getting a numerically exact prediction of the true dynamics.
But whatever errors you are getting due to using DFT or NAMD, may be perfectly okay for what you are wishing to calculate, or if not, the resulting calculation may at least be the best we can do for such a large system at present, with the amount of resources available in the group that has enough interest in the specific problem right now. Better accuracy might be possible for the electronic structure, by using the coupled-cluster method, or GW, or any of a number of other higher-accuracy methods, but they will all have some limitations, and if your system is large enough you might be forced to only use vanilla DFT. Likewise, you can avoid some of the approximations made in Hefei-NAMD and in PYXAID by doing numerically exact quantum dynamics which would be possible with methods like MCTDH or my own program FeynDyn which calculates the dynamics using Feynman integrals, or the HEOM method which converts the same Feynman integrals into systems of differential equations to be numerically solved. But all of these mechanisms that offer a numerically exact quantum dynamics result, again have limitations which cause it to often be worthwhile to just use MD (or maybe NAMD) methods.
It's also possible that for your application, combining DFT and NAMD is not worthwhile, but to be more sure certain of this it would help if we knew precisely what you wanted to calculate, and probably a lot of other information such as how these methods have performed on similar systems or in similar settings.
