ENCUT Convergence Graph Shape and KE Error Subtraction

[emilyherrmann]

Hello,

I am carrying out convergence tests on a primitive cell of Cu 110, and my ENCUT convergence does data does not follow the monotonic decreasing shape I expected. The data is pasted here, and I attached a screenshot of a graph (the yellow vertical lines represent ENMAX from my POTCAR and 1.3 times that ENMAX; the green horizontal line is the converged E0 from running ENCUT = 1500 eV):

ENCUTConvergenceGraph.png

ENCUT (eV) E0 (eV) Total KE Error (eV) E0 - Error (eV)
340 1.7788297 0.559 1.2198297
350 1.7066254 0.412 1.2946254
360 1.656368 0.3176 1.338768
370 1.61637 0.26 1.35637
380 1.5886873 0.2268 1.3618873
390 1.5696191 0.2088 1.3608191
400 1.5568727 0.1992 1.3576727
410 1.5494803 0.1942 1.3552803
420 1.5460972 0.191 1.3550972
430 1.5450792 0.1878 1.3572792
440 1.5454986 0.1842 1.3612986
450 1.5471415 0.1796 1.3675415
460 1.5509194 0.1726 1.3783194
470 1.5552163 0.1638 1.3914163
480 1.5600601 0.1534 1.4066601
490 1.5649083 0.1422 1.4227083
500 1.5694021 0.131 1.4384021
510 1.5732593 0.1196 1.4536593
520 1.5772663 0.1082 1.4690663
530 1.5813783 0.0964 1.4849783
540 1.5859612 0.0846 1.5013612
550 1.5896621 0.0738 1.5158621
560 1.5921237 0.0648 1.5273237
570 1.5937066 0.0574 1.5363066
580 1.5948015 0.051 1.5438015
590 1.5962719 0.0448 1.5514719
600 1.5978221 0.039 1.5588221
610 1.5991327 0.0342 1.5649327
620 1.5998809 0.0304 1.5694809
630 1.6003667 0.0274 1.5729667
640 1.6005178 0.0252 1.5753178
650 1.6006121 0.0234 1.5772121
660 1.6006477 0.0218 1.5788477
670 1.600599 0.0206 1.579999

Currently, my POSCAR is as follows. I am using the Cu_pv POTCAR and a 12x12x12 gamma centered k-point mesh. Eventually I will be adsorbing a molecule of an organic semiconductor on it, but first I wanted to converge values for just the Cu:

Cu110
2.590000
1.02130383981529 -0.00000000000000 0.00000000000000
-0.00000000000000 1.44021611736692 0.00000000000000
0.00000000000000 0.00000000000000 1.02130383981529
Cu
2
Selective Dynamics
Direct
0.00000000000000 0.00000000000000 0.00000000000000 T T T Cu
0.50000000000000 0.50000000000000 0.50000000000000 T T T Cu

My INCAR tags are as follows:

ENCUT = 340
PREC = Accurate
IBRION = -1
NSW = 0
EDIFF = 0.000001
ISMEAR = 0
SIGMA = 0.05
LWAVE=.FALSE.
GGA = ML
LUSE_VDW = .TRUE.
ZAB_VDW = -1.8867
AGGAC = 0.0000
LASPH = .TRUE.

My specific questions are:
1) Why is E0 increasing toward convergence instead of decreasing? If I stop using a van der Waals functional, the E0 becomes negative, but the overall shape is unchanged. Is this indicative of some problem in my system?

2) Why does subtracting the KE error change the early shape so dramatically? I am getting the KE error from the OUTCAR line that reads "kinetic energy error for atom" then subtracting that for each atoms of the species (in this case, I subtracted it twice since I have two Cu). Once I subtract the error, the energy does change mostly monotonically toward convergence, just in the increasing direction instead of the decreasing direction. I have read a tutorial from Danny van Poucke (https://dannyvanpoucke.be/vasp-tutor-co ... esting-en/) that shows similar corrected vs uncorrected behavior to my data, except for at the small ENCUT values.

Thank you!
Emily

[zahedzx]

Hi Emily,

What you observe is actually not unusual for VASP PAW calculations.

1. The total energy is not required to decrease monotonically with increasing ENCUT. The variational principle strictly applies to the wavefunction representation, but in PAW calculations the reported total energy contains additional terms, and the finite-basis-set error does not necessarily produce a strictly monotonic convergence curve. What matters is that the energy approaches a stable limit as ENCUT increases.

2. The "kinetic energy error for atom" term is precisely intended to estimate the finite plane-wave cutoff error. When you subtract this correction from the raw energy, the convergence behavior often becomes much smoother and closer to monotonic, which is exactly what you are observing. In fact, for ENCUT convergence tests it is generally recommended to examine the corrected quantity rather than the raw total energy.

3. In your inputs, you are using:
   GGA = ML
LUSE_VDW = .TRUE.
Cu_pv potential

   These settings introduce additional contributions to the total energy, so expecting a simple textbook monotonic convergence curve may be unrealistic.

4. Since your eventual goal is adsorption on a Cu(110) surface, I would recommend converging energy differences (e.g., adsorption energies or surface energies) rather than the absolute total energy of bulk Cu alone. Often these quantities converge significantly faster with ENCUT due to cancellation of basis-set errors.

Overall, I do not see anything in the data that suggests a problem with the system itself. The corrected energy appears to approach a well-defined limit, which is the main criterion for a successful ENCUT convergence test.

Best,
Zahed