Infrared calculation for bulk systems

[ChiCheng45]

Description of work
Infrared calculation for bulk systems where molecules are not available.

The idea is

where

now we must define what we mean by $j$ close to $i$. I do the following, for each time step I run the minimum image to get all atoms close to $i$. I define $j$ to be close to $i$ if it has been within a specific distance from $i$ at any time across the trajectory.

Closes #650

[ChiCheng45]

Here are the results using DFTB water trajectory using a cutoff of 0.7, 0.5, and 0.2 nm cutoff. Note that the DFTB trajectory is very short so I think the larger cutoff introduces more noise which I think could be reduced with a longer trajectory. Short cutoff should produce results similar to the molecular IR calculation.

[ChiCheng45]

@MBartkowiakSTFC do you have any good test system you want to try this on?

[MBartkowiakSTFC]

@MBartkowiakSTFC do you have any good test system you want to try this on?

I'd suggest the SrTiO3 trajectory, since it is a crystal. Start with charges close to Sr:+1.2, Ti: +0.3, O: -0.5.

[ChiCheng45]

@MBartkowiakSTFC do you have any good test system you want to try this on?

I'd suggest the SrTiO3 trajectory, since it is a crystal. Start with charges close to Sr:+1.2, Ti: +0.3, O: -0.5.

I think there should be issues with periodic systems but anyway here is the result using STO16_80K from one drive. Don't know if that looks any good or not.

Here is the derivative dipole correlation function, the trajectory is probably too short.

Here is the DOS of the same trajectory for reference.

[oerc0122]

Looking good, just a couple of minor things.