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During the convergence test of k points, I observed my energy start increasing instead of decreasing. I am doubtful is this correct or I am doing something wrong. can I take the appropriate K point in this type of converged graph in which energy is inceasing. I am doing this convergence test for bulk material (spin polarised calculation) and K points I took like 2X2X2 then 3X3X3 and so on and observed the corresponding energy.
energy convergence with different K points mesh

Here are my input file settings:

SYSTEM = GRPH Electronic Relaxation 1 ISTART = 0 ICHARG = 2 ISPIN = 2 LWAVE = .F. LELF = .F. MAGMOM = 128*1.0 PREC = Accurate ENCUT = 500 LREAL = A NELM = 100 NELMIN = 4 EDIFF = 1E-5 EDIFFG = -1E-2 NSW = 500 IBRION = 2 ISIF = 3 LORBIT = 10 #DOS related values ISMEAR = 0; SIGMA = 0.05
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  • $\begingroup$ Welcome to our community! $\endgroup$
    – Camps
    Sep 27 at 22:45
  • $\begingroup$ Kindly tell your system, input setting as well for clearity $\endgroup$ Sep 28 at 6:05
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    $\begingroup$ +1 energy should decrease as you change the energy cutoff because it is a variational parameter (you increase the number of plane waves in your basis), but there is no reason why the energy should decrease as a function of the number of k-points, so this looks ok to me. $\endgroup$
    – ProfM
    Sep 28 at 6:22
  • $\begingroup$ It is a bulk system with 68 atoms in the unit cell. Lattice parameter I took from the literature. Here is my input file setting. SYSTEM = GRPH Electronic Relaxation 1 ISTART = 0 ICHARG = 2 ISPIN = 2 LWAVE = .F. LELF = .F. MAGMOM = 128*1.0 PREC = Accurate ENCUT = 500 LREAL = A NELM = 100 NELMIN = 4 EDIFF = 1E-5 EDIFFG = -1E-2 NSW = 500 IBRION = 2 ISIF = 3 LORBIT = 10 #DOS related values ISMEAR = 0; SIGMA = 0.05 $\endgroup$ Sep 28 at 8:27
  • $\begingroup$ +1. Welcome to our new community and thank you for contributing your question here! We hope to see much more of you in the future !!! $\endgroup$ Sep 30 at 21:06
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Let's just remind ourselves what k point sampling is. It is used to approximate the integral of a function over the Brillouin zone by replacing the integral with a sum over a finite number of points: $$ \int_{BZ} F({\bf k})d{\bf k} \approx \sum_j w_j F({\bf k_j}) $$

Now this is an approximation, and for any relatively sane function the error in this approximation will decrease with the number of sampling points, and eventually converge to the correct value. But note there is absolutely nothing which says what the sign of the error is. It could be positive. It could be negative. And whether it is positive or negative could vary with the number of sampling points. Thus it is far from uncommon to see the total Energy increase when you initially increase the number of k points, and then show damped oscillations about the converged value, which is what you seem to be observing.

Compare this with how the total energy changes with respect to variations in the wavefunction. Here the variational principle applies, so any approximate wavefunction will result in a total energy higher than the ground state energy, unless the wavefunction is exactly the ground state wavefunction. Thus we can solve for the ground state wavefunction (and energy) by a minimization procedure. However for k point sampling this principle does not apply, and thus we can see errors of either sign - k point sampling is not variational, but enough k points will converge to the true value (or more strictly to within a desired error from the true value)

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