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In Semiconductor Physics, one of the main parameters of interest is the band gap. It is known that, in DFT, there are functionals that underestimate it.

I came across the MOPAC program, a semi-empirical quantum chemistry program based on Dewar and Thiel's NDDO approximation, that have two utilities to work with periodical system.

The picture bellow shows the bands calculated for $\ce{TiO2}$: enter image description here

The problem is that, as MOPAC is not for periodic systems, it is a little difficult to calculate the bands with it (it is mandatory to leave the calculations windows open and you can not move the mouse). But, the gap was in agreement with the experimental value :).

Is there any other software with semiempirical methods available to calculate the electronic structure of periodical systems?

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    $\begingroup$ I believe you want to look into DFTB methods, which would be the equivalent of semiempirical molecular methods. I see Ti-oxide parameters at DFTB.org $\endgroup$
    – Geoff Hutchison
    Commented May 19, 2020 at 20:59
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    $\begingroup$ My experience with MOPAC is good for molecules, but it's a pain for periodic systems because the unit cell has to be a certain size (e.g., you usually have to generate a supercell). $\endgroup$
    – Geoff Hutchison
    Commented May 19, 2020 at 21:00
  • $\begingroup$ @GeoffHutchison Different implementations of DFTB are indeed very helpful (and fast) to produce band structures and DOS. However, both the method and the parameterization is derived from DFT, therefore it inherits the biases of DFT. $\endgroup$
    – Greg
    Commented May 20, 2020 at 14:55

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DFTB+

One option is DFTB+. It is free, open source, has been around for more than a couple years now, and has a fairly big community.

You are also very lucky, since your question is about the band structure of TiO$_2$ and the sample input that DFTB+ provides for band structure calculations is for... TiO$_2$ :)

The following might also be useful:

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$
    – JNat ♦
    Commented Jun 1, 2020 at 15:04

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