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I am trying to raise the temperature of my model and keep the temperature at 300K, with an NVT ensemble and Nose-Hoover thermostat.
I am doing this job with VASP, here is the INCAR file.

DFT+U Calculation
LDAU   = .TRUE.        (Activate DFT+U)
LDATYPE=  2            (Dudarev; only U-J matters)
LDAUL  =  -1 -1 -1 -1 2 -1        (Orbitals for each species)
LDAUU  =  0 0 0 0  6  0       (U for each species)
LDAUJ  =  0 0 0 0 0 0        (J for each species)
LMAXMIX=  4            (Mixing cut-off; 4-d, 6-f)
 
Global Parameters
ISTART =  1            (Read existing wavefunction; if there)
ISPIN  =  2            (Non-Spin polarised DFT)
#MAGMOM = 4*0 4*0 48*0 24*1 1*1
LREAL  = Auto       (Projection operators: automatic)
ENCUT  =  520        (Cut-off energy for plane wave basis set, in eV)
PREC   =  Normal       (Precision level)
LWAVE  = .FALSE.        (Write WAVECAR or not)
LCHARG = .FALSE.        (Write CHGCAR or not)
ADDGRID= .TRUE.        (Increase grid; helps GGA convergence)
# LVTOT  = .TRUE.      (Write total electrostatic potential into LOCPOT or not)
# LVHAR  = .TRUE.      (Write ionic + Hartree electrostatic potential into LOCPOT or not)
# NELECT =             (No. of electrons: charged cells; be careful)
# LPLANE = .TRUE.      (Real space distribution; supercells)
NCORE   = 8           (Max is no. nodes; dont set for hybrids)
 
Electronic Relaxation
ISMEAR =  0            (Gaussian smearing; metals:1)
SIGMA  =  0.05         (Smearing value in eV; metals:0.2)
NELM   =  90           (Max electronic SCF steps)
NELMIN =  6            (Min electronic SCF steps)
EDIFF  =  1E-06        (SCF energy convergence; in eV)
PREC=Low
ISYM=0
MAXMIX = 40  
IWAVPR=11
############################# MD setting #####################################
# canonic (Nose) MD with XDATCAR updated every 10 steps
IBRION = 0
MDALGO = 2                     รค switch to select thermostat
SMASS =  1                     # Nose mass
ISIF = 2                       # this tag selects the ensemble in combination with the thermostat
NSW =1000
POTIM = 1
TEBEG = 300
TEEND = 300
NBLOCK = 4
##############################################################################

Here is the screenshot of my model:
enter image description here

My question is:
Why does the temperature fluctuate so much during AIMD?

enter image description here

Here is an result after I run 5ps AIMD:
enter image description here

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1 Answer 1

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The primary reason is that your simulation time is too short. To thermally equilibrate a system, the simulation time must be much longer than the period of the slowest phonon mode, so that even the slowest vibration has taken place multiple times. Taking a conservative estimate that the lowest phonon mode of your system is $100 \mathrm{~cm}^{-1}$, we see that the period of this mode is about $300 \mathrm{~fs}$ (note that this correlates very well with the oscillation period of the total energy!), so that you must perform the AIMD for at least a few picoseconds before the slowest vibration damps out.

Another, probably secondary, reason is that any small system will have notable thermal fluctuations even when already equilibrated. Your system is not particularly large, so this inherent thermal fluctuation may also contribute somewhat to the observed fluctuations.

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  • $\begingroup$ I update the result after running AIMD for 5ps, it seems there is a new emerging pattern, which oscillates with a 2500fs period. Does that mean I need to run AIMD for dozens of picoseconds? $\endgroup$
    – Jack
    Commented Apr 23, 2022 at 8:35
  • $\begingroup$ @Jack Maybe this means that my second point is actually the primary reason for the fluctuations, in which case longer simulation times won't help. Let's see if other people can give some estimates on the magnitude of thermal fluctuations due to the small size of the system... $\endgroup$
    – wzkchem5
    Commented Apr 23, 2022 at 10:08
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    $\begingroup$ Another possibility is the use of the Nose-Hoover thermostat. How did you select the thermostat mass? I've read that because the time-evolution of the added variable from the thermostat is described by a second-order equation, heat may flow in and out of the system in an oscillatory fashion, leading to nearly periodic temperature fluctuations with the frequency proportional to the heat bath mass. $\endgroup$
    – Hayden S
    Commented Apr 23, 2022 at 18:06
  • $\begingroup$ If you haven't yet done so, my suggestion is to run a few test simulations with different Nose mass to see how this effects your temperature evolution. It's too bad that more modern thermostats are not available in VASP, as my recommendation is always to use this one: aip.scitation.org/doi/10.1063/1.2408420 $\endgroup$
    – Hayden S
    Commented Apr 23, 2022 at 18:37

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