Implement k-points sampling

[leifjacobson]

This could easily be a feature but I'm filing as an issue in case it's not. As a test I computed the cohesive energy of ammonia crystal (from the X23 test set) using the given unit cell as well as 2x2x2, 3x3x3, etc supercells. The energy I compute is 3.25, 9.25 and 10.10 kcal/mol/molecule for the unitcell, 2x2x2, and 3x3x3 respectively. For larger supercells I get a segfault.

Can you advise? Is this due to lack of k-point sampling (gamma point approx)? Is this expected? Is there a hard limit on the system size?

Molecule geometry:

$coord angs
1.8596000000 1.3558000000 0.5232000000 H
1.3558000000 0.5232000000 1.8596000000 H
0.5232000000 1.8596000000 1.3558000000 H
1.0342000000 1.0342000000 1.0342000000 N
$end                                                

Unit cell geometry:

$coord angs
1.8596000000 1.3558000000 0.5232000000 H
1.3558000000 0.5232000000 1.8596000000 H
0.5232000000 1.8596000000 1.3558000000 H
4.3407000000 1.1253000000 4.4390000000 H
3.8368000000 1.9579000000 3.1025000000 H
3.0043000000 0.6214000000 3.6064000000 H
3.6064000000 3.0043000000 0.6214000000 H
4.4390000000 4.3407000000 1.1253000000 H
1.9579000000 3.1025000000 3.8368000000 H
0.6214000000 3.6064000000 3.0043000000 H
1.1253000000 4.4390000000 4.3407000000 H
3.1025000000 3.8368000000 1.9579000000 H
1.0342000000 1.0342000000 1.0342000000 N
3.5152000000 1.4469000000 3.9280000000 N
3.9280000000 3.5152000000 1.4469000000 N
1.4469000000 3.9280000000 3.5152000000 N
$periodic 3
$lattice angs
4.9621637000 0.0000000000 0.0000000000
0.0000000000 4.9621637000 0.0000000000
0.0000000000 0.0000000000 4.9621637000
$end                                                    

2x2x2 cell

$coord angs                                                                                                                                                                                                                                   
0.5539040000 2.7226850000 -3.7759750000 H                                                                                                                                                                                                     
0.0501040000 1.8900850000 -2.4395750000 H                                                                                                                                                                                                     
-0.7824960000 3.2264850000 -2.9433750000 H                                                                                                                                                                                                    
3.0350040000 2.4921850000 0.1398250000 H                                                                                                                                                                                                      
2.5311040000 3.3247850000 -1.1966750000 H                                                                                                                                                                                                     
1.6986040000 1.9882850000 -0.6927750000 H                                                                                                                                                                                                     
2.3007040000 4.3711850000 -3.6777750000 H                                                                                                                                                                                                     
3.1333040000 5.7075850000 -3.1738750000 H                                                                                                                                                                                                     
0.6522040000 4.4693850000 -0.4623750000 H                                                                                                                                                                                                     
-0.6842960000 4.9732850000 -1.2948750000 H                                                                                                                                                                                                    
-0.1803960000 5.8058850000 0.0415250000 H                                                                                                                                                                                                     
1.7968040000 5.2036850000 -2.3412750000 H                                                                                                                                                                                                     
-0.2714960000 2.4010850000 -3.2649750000 N                                                                                                                                                                                                    
2.2095040000 2.8137850000 -0.3711750000 N                                                                                                                                                                                                     
2.6223040000 4.8820850000 -2.8522750000 N                                                                                                                                                                                                     
0.1412040000 5.2948850000 -0.7839750000 N                                                                                                                                                                                                     
0.5539040000 2.7226850000 1.1861890000 H                                                                                                                                                                                                      
0.0501040000 1.8900850000 2.5225890000 H                                                                                                                                                                                                      
-0.7824960000 3.2264850000 2.0187890000 H                                                                                                                                                                                                     
3.0350040000 2.4921850000 5.1019890000 H                                                                                                                                                                                                      
2.5311040000 3.3247850000 3.7654890000 H                                                                                                                                                                                                      
1.6986040000 1.9882850000 4.2693890000 H                                                                                                                                                                                                      
2.3007040000 4.3711850000 1.2843890000 H                                                                                                                                                                                                      
3.1333040000 5.7075850000 1.7882890000 H                                                                                                                                                                                                      
0.6522040000 4.4693850000 4.4997890000 H                                                                                                                                                                                                      
-0.6842960000 4.9732850000 3.6672890000 H                                                                                                                                                                                                     
-0.1803960000 5.8058850000 5.0036890000 H                                                                                                                                                                                                     
1.7968040000 5.2036850000 2.6208890000 H                                                                                                                                                                                                      
-0.2714960000 2.4010850000 1.6971890000 N                                                                                                                                                                                                     
2.2095040000 2.8137850000 4.5909890000 N                                                                                                                                                                                                      
2.6223040000 4.8820850000 2.1098890000 N                                                                                                                                                                                                      
0.1412040000 5.2948850000 4.1781890000 N                                                                                                                                                                                                      
0.5539040000 7.6848490000 -3.7759750000 H                                                                                                                                                                                                     
0.0501040000 6.8522490000 -2.4395750000 H                                                                                                                                                                                                     
-0.7824960000 8.1886490000 -2.9433750000 H                                                                                                                                                                                                    
3.0350040000 7.4543490000 0.1398250000 H                                                                                                                                                                                                      
2.5311040000 8.2869490000 -1.1966750000 H                                                                                                                                                                                                     
1.6986040000 6.9504490000 -0.6927750000 H                                                                                                                                                                                                     
2.3007040000 9.3333490000 -3.6777750000 H                                                                                                                                                                                                     
3.1333040000 10.6697490000 -3.1738750000 H                                                                                                                                                                                                    
0.6522040000 9.4315490000 -0.4623750000 H                                                                                                                                                                                                     
-0.6842960000 9.9354490000 -1.2948750000 H                                                                                                                                                                                                    
-0.1803960000 10.7680490000 0.0415250000 H                                                                                                                                                                                                    
1.7968040000 10.1658490000 -2.3412750000 H                                                                                                                                                                                                    
-0.2714960000 7.3632490000 -3.2649750000 N                                                                                                                                                                                                    
2.2095040000 7.7759490000 -0.3711750000 N                                                                                                                                                                                                     
2.6223040000 9.8442490000 -2.8522750000 N                                                                                                                                                                                                     
0.1412040000 10.2570490000 -0.7839750000 N                                                                                                                                                                                                    
0.5539040000 7.6848490000 1.1861890000 H                                                                                                                                                                                                      
0.0501040000 6.8522490000 2.5225890000 H                                                                                                                                                                                                      
-0.7824960000 8.1886490000 2.0187890000 H                                                                                                                                                                                                     
3.0350040000 7.4543490000 5.1019890000 H                                                                                                                                                                                                      
2.5311040000 8.2869490000 3.7654890000 H
1.6986040000 6.9504490000 4.2693890000 H
2.3007040000 9.3333490000 1.2843890000 H
3.1333040000 10.6697490000 1.7882890000 H
0.6522040000 9.4315490000 4.4997890000 H
-0.6842960000 9.9354490000 3.6672890000 H
-0.1803960000 10.7680490000 5.0036890000 H
1.7968040000 10.1658490000 2.6208890000 H
-0.2714960000 7.3632490000 1.6971890000 N
2.2095040000 7.7759490000 4.5909890000 N
2.6223040000 9.8442490000 2.1098890000 N
0.1412040000 10.2570490000 4.1781890000 N
5.5160680000 2.7226850000 -3.7759750000 H
5.0122680000 1.8900850000 -2.4395750000 H
4.1796680000 3.2264850000 -2.9433750000 H
7.9971680000 2.4921850000 0.1398250000 H
7.4932680000 3.3247850000 -1.1966750000 H
6.6607680000 1.9882850000 -0.6927750000 H
7.2628680000 4.3711850000 -3.6777750000 H
8.0954680000 5.7075850000 -3.1738750000 H
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4.2778680000 4.9732850000 -1.2948750000 H
4.7817680000 5.8058850000 0.0415250000 H
6.7589680000 5.2036850000 -2.3412750000 H
4.6906680000 2.4010850000 -3.2649750000 N
7.1716680000 2.8137850000 -0.3711750000 N
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5.1033680000 5.2948850000 -0.7839750000 N
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7.5844680000 4.8820850000 2.1098890000 N
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4.2778680000 9.9354490000 -1.2948750000 H
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4.6906680000 7.3632490000 -3.2649750000 N
7.1716680000 7.7759490000 -0.3711750000 N
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5.1033680000 10.2570490000 -0.7839750000 N
5.5160680000 7.6848490000 1.1861890000 H
5.0122680000 6.8522490000 2.5225890000 H
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7.1716680000 7.7759490000 4.5909890000 N
7.5844680000 9.8442490000 2.1098890000 N
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$lattice angs
9.9243278503 0.0000000000 0.0000000000
0.0000000000 9.9243278503 0.0000000000
0.0000000000 0.0000000000 9.9243278503

[awvwgk]

You can use xTB in DFTB+ with k-point sampling instead of building supercells.

Also, there is no limit in systemsize, but since we are using a shared memory parallelization you have to provide enough memory for all the threads using the OMP_STACKSIZE environment variable, otherwise it the OMP stack might overflow and the program crash.

[leifjacobson]

Thanks for the comment. Sounds like it's a feature. I'll try building DFTB+.

[awvwgk]

Implementing k-point sampling here in tblite would be a really cool feature, but with the integration in DFTB+ we already have such an implementation with both k-points and spin channels available. Therefore, this is currently less of a priority for me.

If more projects start using tblite's high-level API to evaluate xTB singlepoints for periodic systems this might be worth revisiting.

[leifjacobson]

Hi @awvwgk as a follow up I got dftb+ to compile and for the same system described above it looks like convergence is pretty rapid with a pretty small MP kpoint mesh. However, the converged results do not agree with the largest supercell energy reported above. The gamma point and molecular energies do agree to high precision. Do you have some example crystals with GFN2-xTB energies that you believe are converged? It would be useful for me to make sure I'm getting the right answers.

[vladislavivanistsev]

Implementing k-point sampling here in tblite would be a really cool feature, but with the integration in DFTB+ we already have such an implementation with both k-points and spin channels available. Therefore, this is currently less of a priority for me.

If more projects start using tblite's high-level API to evaluate xTB singlepoints for periodic systems this might be worth revisiting.

I have been testing tblite, DFTB+, and CP2k for a while. tblibe as a stand-alone calculator is the most attractive. Yet, it does luck some features, like k-point sampling.
How difficult is to implement k-points?
How about linking the corresponding module to https://pypi.org/project/kpLib/?

[awvwgk]

For me it was easiest to get a good k-point implementation by integrating tblite in DFTB+ and leverage the available k-point aware SCF. For an implementation in tblite we can rely on an external library, but it has to be available in the SCF (so in Fortran) to be useful.