Gamma dynamical matrix does in fact require supercells

[ExpHP]

I don't know how on earth something like this slipped by, but upon reviewing the code I have a very hard time seeing how DefaultDispFn is correct for small unit cells.

As far as I can tell, the current implementation will displace all images of an atom!

This is...very not cool.

[ExpHP]

I believe this affects all data of sufficiently small unit cells that used the rsp2 disp-finder, ever, unless phonons.supercell was used. (and I haven't used it in a long time!)

When I switched the unit tests to stop using phonopy, I think some of the frequencies changed by about 0.02 eV. I assumed it was a chaotic effect from relaxing into a different state, but in hindsight that makes no sense (the simple tests don't relax along eigenvectors). That change was probably due to this bug. Nope, that's not related because that test was already giving phonopy a supercell of target: [0,0,0].

[ExpHP]

Evidence:

function() run {
    cargo run --release --bin=rsp2 -- \
        -c ../tests/resources/defaults.yaml \
        -c ../tests/resources/simple.yaml \
        ../tests/resources/simple.vasp \
        "$@"
}
run -c 'phonons.supercell.~~REPLACE~~.target:[0,0,0]' -o out-1
run -c 'phonons.supercell.~~REPLACE~~.target:[35,35,35]' -o out-2
run -c 'phonons.supercell.~~REPLACE~~.target:[70,70,70]' -o out-3

out-1/eigenvalues.final

# (C)    Frequency(cm-1)        Acou RamnA RamnB  X    Y    Z  
  (T)    0.00007573708821266394 1.00 2e-23 2e-23 0.00 0.00 1.00
  (T)    0.00027612600568365224 1.00 2e-25 2e-25 0.00 1.00 0.00
  (T)    0.0002770808164830437  1.00 3e-25 3e-25 1.00 0.00 0.00
  (-)   19.726084222003376      0.00 5e-5  5e-5  0.31 0.69 0.00
  (-)   19.72608422200816       0.00 5e-5  5e-5  0.69 0.31 0.00
  (-)   84.07792977084624       0.00 1e-7  1e-7  0.00 0.00 1.00
  (-)  963.3600027716088        0.00 3e-27 2e-27 0.00 0.00 1.00
  (-)  967.560958064369         0.00 2e-4  1e-4  0.00 0.00 1.00
  (-) 1667.0423926213853        0.00 1e0   1e0   0.00 1.00 0.00
  (-) 1667.0423926213869        0.00 1e0   1e0   1.00 0.00 0.00
  (-) 1667.6776661642089        0.00 8e-25 7e-25 0.00 1.00 0.00
  (-) 1667.6776661642095        0.00 1e-26 1e-26 1.00 0.00 0.00

out-2/eigenvalues.final

# (C)    Frequency(cm-1)         Acou RamnA RamnB  X    Y    Z  
  (T)   -0.000033616796776970064 1.00 0     0     0.00 0.00 1.00
  (T)    0.00044366861095801127  1.00 1e-24 1e-24 0.00 1.00 0.00
  (T)    0.000444724812062967    1.00 6e-26 5e-26 1.00 0.00 0.00
  (-)   19.71801444586797        0.00 5e-5  5e-5  0.01 0.99 0.00
  (-)   19.7180144458915         0.00 5e-5  5e-5  0.99 0.01 0.00
  (-)   84.1209627770934         0.00 1e-7  1e-7  0.00 0.00 1.00
  (-)  963.3618866402196         0.00 3e-27 2e-27 0.00 0.00 1.00
  (-)  967.5628372822749         0.00 2e-4  1e-4  0.00 0.00 1.00
  (-) 1666.9925961079614         0.00 1e0   1e0   0.00 1.00 0.00
  (-) 1666.9925961079623         0.00 1e0   1e0   1.00 0.00 0.00
  (-) 1667.627888125847          0.00 1e-24 9e-25 0.00 1.00 0.00
  (-) 1667.6278881258481         0.00 4e-26 4e-26 1.00 0.00 0.00

out-3/eigenvalues.final

# (C)    Frequency(cm-1)        Acou RamnA RamnB  X    Y    Z  
  (T)    0.00004174824200528189 1.00 4e-24 4e-24 0.00 0.00 1.00
  (T)    0.00019640518291168715 1.00 1e-23 1e-23 0.01 0.99 0.00
  (T)    0.0001972130445849585  1.00 2e-24 2e-24 0.99 0.01 0.00
  (-)   19.718014446684876      0.00 5e-5  5e-5  0.00 1.00 0.00
  (-)   19.71801444669673       0.00 5e-5  5e-5  1.00 0.00 0.00
  (-)   84.12096277714397       0.00 1e-7  1e-7  0.00 0.00 1.00
  (-)  963.3618866402364        0.00 3e-27 2e-27 0.00 0.00 1.00
  (-)  967.5628372822955        0.00 2e-4  1e-4  0.00 0.00 1.00
  (-) 1666.9925961183683        0.00 1e0   1e0   0.00 1.00 0.00
  (-) 1666.9925961183687        0.00 1e0   1e0   1.00 0.00 0.00
  (-) 1667.6278881362914        0.00 7e-25 6e-25 0.00 1.00 0.00
  (-) 1667.627888136292         0.00 9e-27 9e-27 1.00 0.00 0.00

out-1 and out-2 match up to only 3 sig figs, but out-2 and out-3 match up to about 10 sig figs. This indicates that out-1 is affected by the movement of periodic images.

[ExpHP]

Okay, so this is not high priority because you can fix it with phonons.supercell. (Good thing I didn't remove that!)

It is not a bug in the code because there's no way to work around the supercell requirement for lammps and DFTB+.

It is however a bug in the documentation. The documentation needs to be fixed so that it no longer claims that gamma point does not require a supercell.

[ExpHP]

Okay, I fixed all the mentions I could find in the documentation and comments, but this one's a puzzler:

https://github.com/ExpHP/rsp2/blob/4455eca2ef1124f77551d0c2f2a42c2b7c296d37/tests/force-constants.rs#L189-L203

How is that check succeeding with such a small tolerance? How on earth did I even generate those force constants files, anyways?