'BCONNECT = 1' fails at path break

[irrotational]

Dear Dr. Tadano,

I'm running a simple test calculation on PbTe (no LO/TO splitting included here).

A calculation of the harmonic bands (2x2x2 supercell) gives the following dispersion, when BCONNECT = 1 is used:

There is a path break between U and K. As can be seen, the band-ordering algorithm swaps the order of bands at the U/K break; I have separately done a harmonic calculation with Quantum Espresso and also CASTEP, and both suggest that the bands should be connected across the U/K break. Note that within each path segment (notably along the X-U line), band crossings are indeed correctly detected. The &kpoint field for this calculation was:

&kpoint
  1  # KPMODE = 1: line mode
  G 0.000  0.000  0.000    X 0.500  0.000  0.500    200
  X 0.500  0.000  0.500    U 0.625  0.250  0.625    71
  K 0.375  0.375  0.750    G 0.000  0.000  0.000    212
  G 0.000  0.000  0.000    L 0.500  0.500  0.500    173
  L 0.500  0.500  0.500    W 0.500  0.250  0.750    141
  W 0.500  0.250  0.750    X 0.500  0.000  0.500    100
/

Now, if I repeat the calculation with the exact same input, but instead of a break, create a very short path between U and K (so no longer a true break), like:

&kpoint
  1  # KPMODE = 1: line mode
  G 0.000  0.000  0.000    X 0.500  0.000  0.500    200
  X 0.500  0.000  0.500    U 0.625  0.250  0.625    71
  U 0.625  0.250  0.625    K 0.375  0.375  0.750    3
  K 0.375  0.375  0.750    G 0.000  0.000  0.000    212
  G 0.000  0.000  0.000    L 0.500  0.500  0.500    173
  L 0.500  0.500  0.500    W 0.500  0.250  0.750    141
  W 0.500  0.250  0.750    X 0.500  0.000  0.500    100
/

I get:

(the U and K labels are now overlapping, as there is no longer a true break there)

This perfectly matches the band-connected dispersions I get from Quantum Espresso and CASTEP.

If I set BCONNECT = 2 for the first case, I can see at the U and K points in the .connection file:

#  G X U K G L W X
# 0.000000 0.505969 0.684856 0.684856 1.221517 1.659699 2.017473 2.270458
# k-axis, mapping
...
...
0.684856    2    3    1    6    5    4
0.684856    1    2    3    4    6    5
...
...

(where I've omitted irrelevant lines). As can be seen, the algorithm seems to be incorrectly reordering the bands across the break.

[ttadano]

Thanks for reporting the issue. This happens because the algorithm uses only the similarity of the eigenvectors between consecutive k points, not the similarity of the eigenvalues (frequencies). This part can be improved in the future version.

For your particular case, I've found that the following modification resulted in the expected results.

K -0.375  -0.750 -0.375 G 0.000  0.000  0.000    212

[irrotational]

Hey Dr Tadano,

Thanks so much for your swift response. I did try your suggestion, and it does now correctly join one of the bands across the U/K break (the blue band), but several of the other bands are still incorrectly swapped:

Anyhow, if there is no other fix for now, I can just wait until this is improved in a later version.

[irrotational]

Dear Dr Tadano,

Further to my post above, I would like to ask if BCONNECT = 1 works for SCPH band calculations.

For a 2x2x2 supercell of cubic BaTiO3 (no LO/TO splitting), I get the following SCPH dispersion at 300 K with BCONNECT = 1:

(note that there is no path break here; this is a separate issue to that outlined above).

As can be seen, the bands are not properly connected at any of the crossings; it is as if BCONNECT = 0. The corresponding harmonic calculation - not shown here - has the bands correctly joined up (although there are imaginary modes of course, as cubic BaTiO3 is dynamically unstable within the HA).

If this is a genuine bug I am happy to open a separate issue, it just seemed sensible to mention it here. Perhaps the answer is simply that BCONNECT isn't implemented for the SCPH bands (?).