convergence & cutoff madness
Toon Verstraelen
Dear CP2K users,
I'm running a few basic tests to get a better understanding of the
relation between SCF convergence and the plane wave cutoff. The table
below summarizes a series of trivial energy calculations with different
cutoffs. The input files are attached.
The system in the input is MIL-53-Al, a well-known metal-organic
framework. To keep things simple, I've used a very minimal basis
(SZV-GTH). The largest basis set exponent is 8.3744350009, which
corresponds to a cutoff of 330 Rydberg. (if not mistaken). The
functional is blyp.
There are two weird things in this table:
1) The lowest energy is not obtained with the highest cutoff. It gets
worse above 320.
2) For some high cutoff's there is no SCF convergence. For the low
range, up to 150, this is normal. I would not expect this for a cutoff
of 330.
Does somebody know what is going on? The input files are rather simple,
but maybe I've put in something pernicious? With larger basis sets,
there are more cases where the SCF convergence fails. It becomes
practically useless, even when a decent initial guess with a smaller
basis set is constructed.
Number of failed SCF 10
cutoff [Ry] energy [kjmol] time [s] #iters time per iter [s]"
100.0 370146.36 841.59 250 3.37
110.0 4309.36 1023.83 250 4.10
120.0 4311.87 1053.45 250 4.21
130.0 1159.84 1099.50 250 4.40
140.0 939.17 1166.17 250 4.66
150.0 2549.48 1206.51 250 4.83
160.0 804.26 227.56 42 5.42
170.0 354.60 159.26 29 5.49
180.0 412.98 177.18 29 6.11
190.0 685.96 1455.42 250 5.82
200.0 79.06 199.92 32 6.25
210.0 79.17 262.35 40 6.56
220.0 78.54 201.22 28 7.19
230.0 86.04 218.52 28 7.80
240.0 63.43 261.85 35 7.48
250.0 33.38 2067.27 250 8.27
260.0 34.90 2237.25 250 8.95
270.0 22.10 225.49 28 8.05
280.0 14.48 458.72 52 8.82
290.0 5.22 322.73 32 10.09
300.0 4.17 251.49 28 8.98
310.0 6.07 319.30 32 9.98
320.0 0.00 296.63 29 10.23
330.0 2.18 2370.99 250 9.48
340.0 4.32 351.99 28 12.57
350.0 4.38 398.81 32 12.46
360.0 4.37 332.36 25 13.29
370.0 8.01 496.19 39 12.72
380.0 8.10 368.99 29 12.72
390.0 13.16 402.97 29 13.90
400.0 12.49 410.13 29 14.14
cheers,
Toon
Toon Verstraelen
Apparently the smear option does help a little with the convergence, but
it is not yet the solution for everything. I've added these lines to the
SCF section:
ADDED_MOS 12
&SMEAR
METHOD FERMI_DIRAC
ELECTRONIC_TEMPERATURE 300
&END SMEAR
I'm not sure if these parameters are decent, but the table looks
somewhat better for higher cutoffs:
Number of failed SCF 10
100.0 369302.38 381.62 250 1.53
110.0 4309.36 470.68 250 1.88
120.0 4311.87 491.38 250 1.97
130.0 1159.26 517.84 250 2.07
140.0 939.17 503.57 250 2.01
150.0 2550.13 590.24 250 2.36
160.0 804.26 105.18 39 2.70
170.0 354.60 72.56 28 2.59
180.0 412.98 673.03 250 2.69
190.0 410.19 109.42 39 2.81
200.0 79.06 146.17 39 3.75
210.0 79.17 109.10 28 3.90
220.0 78.54 283.20 66 4.29
230.0 86.04 1080.76 250 4.32
240.0 63.43 1099.63 250 4.40
250.0 33.38 431.16 87 4.96
260.0 34.90 1060.15 250 4.24
270.0 22.10 562.68 111 5.07
280.0 14.48 294.24 52 5.66
290.0 5.22 202.16 32 6.32
300.0 4.17 173.59 32 5.42
310.0 6.07 194.87 32 6.09
320.0 0.00 200.38 32 6.26
330.0 2.18 148.32 32 4.63
340.0 4.32 184.79 32 5.77
350.0 4.38 327.02 42 7.79
360.0 4.37 244.75 29 8.44
370.0 8.01 334.95 39 8.59
380.0 8.10 226.42 32 7.08
390.0 13.16 239.73 32 7.49
400.0 12.49 247.45 32 7.73
In bottom of the table, the computations are faster and all converge.
Converged energies do still match with the other table. I'm still not
sure why the energy increases for the higher cutoffs. It is also
surprising that a cutoff of 250 does not lead to convergence while
several lower values do...
cheers,
Toon
Toon Verstraelen
Below a similar table with the DZVP-GTH basis instead of the SZV-GTH basis.
Number of failed SCF 7
110.0 1849.77 159.59 42 3.80
120.0 1849.20 129.75 35 3.71
130.0 986.17 210.71 54 3.90
140.0 823.57 489.46 114 4.29
150.0 762.08 130.94 30 4.36
160.0 604.84 521.14 113 4.61
170.0 294.25 176.77 37 4.78
180.0 319.16 1270.09 250 5.08
190.0 323.22 1198.53 250 4.79
200.0 87.76 1330.97 250 5.32
210.0 87.63 1330.64 250 5.32
220.0 83.83 1375.40 250 5.50
230.0 90.91 630.85 104 6.07
240.0 74.54 552.09 87 6.35
250.0 41.28 207.62 30 6.92
260.0 39.96 1330.75 250 5.32
270.0 24.73 598.13 89 6.72
280.0 16.34 237.48 29 8.19
290.0 5.94 285.42 31 9.21
300.0 4.92 303.03 34 8.91
310.0 7.34 628.55 86 7.31
320.0 0.00 453.03 57 7.95
330.0 1.91 250.62 26 9.64
340.0 4.26 287.63 27 10.65
350.0 5.16 239.20 23 10.40
360.0 5.30 341.52 35 9.76
370.0 8.57 303.73 26 11.68
380.0 8.52 286.88 24 11.95
390.0 12.97 262.10 24 10.92
400.0 12.20 289.96 26 11.15
It is a bit strange that the timings improve and convergence is
obtained with less steps compared to the smaller basis.
We also did similar tests with the PBE functional. All those
computations ran smoothly without any convergence issue.
Citeren Toon Verstraelen <Toon.Ver...@UGent.be>:
Fawzi Mohamed
some comments:
1) do you trust your cp2k version, can you reproduce the regtest
results within a reasonable error?
2) convergence wrt. cutoff is not variational
3) if the cutoff is too low derivatives (and KS matrix) are wrong, and
thus convergence difficult (I would say the lowest cutoff is around
280 for your case)
4) using multiple grids you should increase also the relative cutoff
to really go at convergence.
I hope this helps making sense of your data
Fawzi
Toon Verstraelen
> Hi,
>
> some comments:
> 1) do you trust your cp2k version, can you reproduce the regtest
> results within a reasonable error?
> 2) convergence wrt. cutoff is not variational
> 3) if the cutoff is too low derivatives (and KS matrix) are wrong, and
> thus convergence difficult (I would say the lowest cutoff is around
> 280 for your case)
> 4) using multiple grids you should increase also the relative cutoff
> to really go at convergence.
Thansk for all the comments! I'll check the tests first.
best regards,
Toon