# Tight binding model for nanoparticles as finite systems

I'm still trying to calculate the band structure ab initio for some hypothetical nanoparticles. It seems that I can directly build a tight-binding model by forming Bloch functions, numerically calculate the dispersion relation, and then apply Brus equation to get band gaps for nanoparticles.

Another strategy I've tried is just to treat the nanoparticle as a large molecule and use MO calculation; however, the problem is that the matrix grows too large when working in three dimensions and using basis sets with multiple orbitals (consider a $$20 × 20 × 20$$ cubic lattice with $$\mathrm{sp^3d}$$ basis, that should be a whooping $$20^3 · 5^2 = 200\ 000 × 200\ 000$$ matrix).

I'm asking if there's some modified version of tight-binding model that specifically work for finite systems. I'm aware that tight-binding model can be used to study nanowires, but the wires themselves are assumed to be infinitely long in one direction so that's not quite what I want.

My chemistry professor suggested modifying the Bloch functions using wavefunctions that are solutions to the particle in a box model. However, I'm not sure how to do this properly, or what's the justification for this.

• I'm not sure I understood all of what you are writing. If you can treat nanoparticles as molecules, then the xtb program might be worth having a look at: github.com/grimme-lab/xtb To my knowledge, it works fairly well for extensive biomolecules. – Martin - マーチン Dec 6 '19 at 2:35
• @Martin-マーチン Thank you! I will look into this. It seems to be helpful for me. – Macrophage Dec 6 '19 at 2:37
• If the software helped you, I would very much appreciate it, if you could write a short answer with an example how to do it for the future generations to come. – Martin - マーチン Dec 6 '19 at 13:24