Question About Energy Fluctuations in AIMD

[flamingoXu]

I found your work very interesting and have been trying to reproduce your procedure in an MoS₂ system. However, in my NVE runs at 50 K (using the same supercell and the INCAR settings you provided), I observe energy fluctuations that are significantly larger than those reported in your paper. Could you please confirm whether it is necessary to enable spin–orbit coupling (SOC) or to use a denser k-point mesh during the heating and NVE stages to achieve the reported stability?

Thank you for your time and assistance.

[Ionizing]

There are two points:

1. For MoS2 (or MoSe2 maybe) system, SOC doesn't have considerable effect on atomic structure, meaning that under NVE stage, we don't need to open it. But, there is spin-valley locking feature in this system, which requires us to consider the SOC effect in the many WAVECAR calculation stage.

2. It is possible that energy fluctuation for MoS2 is larger than MoSe2, since Se (~79amu) is heavier than S (~32amu). It means that in the same temperature $T$, S atom displacements $x$ are larger than Se, as is shown in the displacement formula $\langle x^2 \rangle = k_BT / M\omega^2$. Larger displacement leads to larger distortion, and may result in larger energy shift.
   In fact, from the paper Jiang et al., Sci. Adv. 2021; 7: eabf3759(although under 100 K) Fig. 3A, the energy fluctuations for MoS2 VBs are larger than MoSe2 VB shown in Adv. Optical Mater. 2025, 2403069 Figure 1b.

Anyway, I don't think you need to open SOC in NVE stage, and denser K-point mesh may do no help to reduce the energy fluctuation.

There may be some flaw in my thought, and I'm happy that you could point it out if possible.

[flamingoXu]

Thank you for your suggestion. I compared my results with those reported by Jiang et al. in Sci. Adv. (2021), and I still observe significantly larger fluctuations. Would you be able to share the POSCAR file used in Jiang et al., Sci. Adv. 2021? The choice of supercell may be having an important effect. Thank you.

[Ionizing]

Actually, the supercell I used is same as Jiang's, and the only differences are the element types and lattice constant (with relaxation). Would you please show your input files, including POSCAR, INCAR (or any other necessary files) for further debugging?

[flamingoXu]

Thank you for yous response,the is some input_files:
INCAR:
Global Parameters
ISTART = 1 (Read existing wavefunction, if there)
ISPIN = 1 (Non-Spin polarised DFT)

ICHARG = 11 (Non-self-consistent: GGA/LDA band structures)

LREAL = auto (Projection operators: automatic)
ENCUT = 500 (Cut-off energy for plane wave basis set, in eV)
LWAVE = F (Write WAVECAR or not)
LCHARG = F (Write CHGCAR or not)
PREC = MED

Electronic Relaxation
ISMEAR = 0
SIGMA = 0.05
EDIFF = 1E-05
NCORE = 8
Molecular Dynamics
IBRION = 0 (Activate MD)
NSW = 8000 (Max ionic steps)
#EDIFFG = -1E-02 (Ionic convergence, eV/A)
POTIM = 1 (Timestep in fs)
SMASS = -3 (MD Algorithm: -3-microcanonical ensemble, 0-canonical ensemble)
#TEBEG = 50 (Start temperature K)
#TEEND = 50 (Final temperature K)

MDALGO = 1 (Andersen Thermostat)

POTIM = 1
ISYM = 0 (Switch symmetry off)
#NWRITE = 0 (For long MD-runs use NWRITE=0 or NWRITE=1)
IVDW =12
NBLOCK = 1
IWAVPRE=11

POSCAR_NVE
Mo Se
1.00000000000000
9.4667999999999992 5.4676000000000000 0.0000000000000000
-4.7377000000000002 8.2053999999999991 0.0000000000000000
0.0000000000000000 0.0000000000000000 15.0000000000000000
Mo S
12 24
Direct
0.9143826962379409 0.8347623866985960 0.5006961843847898
0.6644469287840151 0.6652375888405085 0.5007808824074184
0.9139049321220385 0.1651351493776012 0.5012621711282677
0.9130058823892814 0.4996953956452715 0.4995270229588844
0.1640554093984050 0.6650094438151245 0.5004287430466755
0.1642638308178353 0.3350099251192388 0.5005184836373330
0.1628794767748929 0.9995261069332270 0.4999856704054813
0.6639760563686762 0.3348243227747906 0.5009140495380034
0.6629472996714904 0.9994501509269942 0.4995461623564928
0.4140154722674088 0.1651910871567555 0.5004740419102045
0.4129661574324882 0.4996420555733742 0.5001451601926968
0.4140503195731148 0.8350870780401624 0.5010753716314106
0.7483777973322181 0.5000856621630732 0.6041751154813626
0.7484465310600080 0.8332792672096734 0.3943298941223464
0.7477965036109521 0.8324155191423164 0.6069754667745793
0.4969081686726398 0.6668887357647042 0.6066061891895355
0.4987021326398616 0.6677026020538525 0.3937219632438998
0.7476689901102923 0.1683345491361928 0.6067363863291030
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0.2477193557421415 0.8330140207227181 0.3937801731559538
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0.2479393443992635 0.5000304745330498 0.3975657230222853
0.2486138210018873 0.5001846577118748 0.6041006842900819
0.9964563984001629 0.6672778575451881 0.6069748818621936
0.2484723123191100 0.1677294908250994 0.3941289480987357
0.2471030975432925 0.1667811380643479 0.6072168944111225
0.9982636417449816 0.6676390508653018 0.3939906642952005
0.9989462849373604 0.3330619894294968 0.3940136515143658
0.9979806738924284 0.3323470739349842 0.6064047734060029
0.9983163911593076 0.0000595739643527 0.6038211969808980
0.9978291879331805 0.9995783560096060 0.3970995050474420

-0.62596213E-03 -0.39828520E-03 -0.84562756E-03
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-0.49890672E-03 -0.49544605E-03 -0.80028860E-03
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-0.62273042E-03 -0.34787355E-03 -0.68461214E-03
-0.72302042E-03 -0.42270838E-03 -0.92067059E-03
-0.65830247E-03 -0.35815040E-03 -0.45492282E-03
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0.77506817E-03 0.84899839E-03 -0.27043626E-03
0.12444356E-02 0.15665755E-02 0.22016611E-02
0.53521885E-03 0.42548758E-03 -0.70174439E-03
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0.59564895E-03 0.35244576E-03 -0.32503395E-03
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0.35427213E-03 -0.53411531E-03 0.23813919E-02
0.11262924E-02 0.16835944E-02 0.22487381E-02
0.76249299E-03 0.40295480E-03 -0.32318777E-03
0.40004151E-03 -0.26774534E-03 0.21142981E-02
0.54781896E-03 0.75993157E-03 -0.13392179E-04
0.81031648E-03 0.30779968E-03 -0.46723637E-03
0.13062610E-02 0.16016820E-02 0.21840498E-02
0.41355569E-03 -0.33819629E-03 0.19856980E-02
0.53148066E-03 0.72356078E-03 0.64381130E-04
0.42136681E-03 0.24087428E-03 -0.59957587E-03
0.20413596E-02 0.55200521E-03 0.24777301E-02
0.50345825E-03 0.46688177E-03 -0.50279637E-03
0.17824734E-02 0.64865699E-03 0.24735235E-02
0.14948292E-02 0.16762075E-02 0.23077805E-02
0.73636083E-03 0.43277609E-03 -0.45366470E-03
0.72038100E-03 0.79518770E-03 0.14930670E-03
0.52402388E-03 -0.16212722E-03 0.21209705E-02

       1

1.00000000000000
0.10000000E+01 0.00000000E+00 0.00000000E+00 0.00000000E+00
0.91431489E+00 0.83475903E+00 0.50063981E+00
0.66439243E+00 0.66523122E+00 0.50073888E+00
0.91384275E+00 0.16511620E+00 0.50120882E+00
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0.66391228E+00 0.33482877E+00 0.50084923E+00
0.66288836E+00 0.99944472E+00 0.49952361E+00
0.41394166E+00 0.16517311E+00 0.50042604E+00
0.41290401E+00 0.49964317E+00 0.50011443E+00
0.41398491E+00 0.83508935E+00 0.50101786E+00
0.74847803E+00 0.50012234E+00 0.60415709E+00
0.74861676E+00 0.83335675E+00 0.39447667E+00
0.74785836E+00 0.83242615E+00 0.60692868E+00
0.49694866E+00 0.66688851E+00 0.60658298E+00
0.49886867E+00 0.66766283E+00 0.39389800E+00
0.74773230E+00 0.16833532E+00 0.60671472E+00
0.74809580E+00 0.16707665E+00 0.39393734E+00
0.74767973E+00 0.50011554E+00 0.39757266E+00
0.24788558E+00 0.83310844E+00 0.39393009E+00
0.24728932E+00 0.83327977E+00 0.60626561E+00
0.49864183E+00 0.25978066E-03 0.39780156E+00
0.49825667E+00 0.79733865E-03 0.60439470E+00
0.49763307E+00 0.33340146E+00 0.60616151E+00
0.49850549E+00 0.33297720E+00 0.39425576E+00
0.24795664E+00 0.49997774E+00 0.39769810E+00
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0.99650079E+00 0.66727763E+00 0.60693491E+00
0.24865927E+00 0.16767219E+00 0.39429413E+00
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[Ionizing]

The INCAR looks nice. And it seems there is nothing wrong with POSCAR.

Jiang just gave the POSCAR for MoS2 primitive cell:

MoS2                                    
   1.00000000000000     
     2.7565588602458653   -1.5914999999999984    0.0000000000000000
     0.0000000000000000    3.1829999999999998    0.0000000000000000
     0.0000000000000000    0.0000000000000000   25.0000000000000000
   S    Mo
     2     1
Direct
 -0.0000000000000000  0.0000000000000000  0.4374561483394361
  0.0000000000000000  0.0000000000000000  0.5625438516605639
  0.6666666666666643  0.3333333333333357  0.5000000000000000

Hope it helps.