# Re: [QE-users] NVE simulation in cp.x - large fluctuation in temperature

Dear Jie Peng,

suppose you were running a model harmonic system in 1 dimension.

M a = - K x

at fixed energy  E.


The kinetic energy would fluctuate harmonically between 0 (at maximum/minimum elongation) and E at the equilibrium distance .


On average the Kinetic energy would be E/2 and its fluctuation some big fraction of E^2


Something like sigma^2 = 1/T \int_0^T (E cos^2(2pi t/T) -E/2)^2 dt = E^2 1/T \int_0^T (cos(4pi t/T)/2)^2 dt = (E/2)^2 1/2pi \int_0^2pi cos^2(x) dx = (E/2)^2 / 2

or

sigma =  1/sqrt(2) * E/2 = 1/sqrt(2) avg EKin


with 1 degree of freedom the mean square fluctuation of the kinetic energy is 70% of its average !


you have 3 atoms in your cell hence 9 degrees of freedom. Assuming each contributes independently to the average this goes down by a factor 1/sqrt(9)=1/3


actually more likely just 1/sqrt(6) as the total momentum is conserved so only 6 modes at Gamma are actually excited...


If you perform your simulation in a bigger supercell with more atoms (more degrees of freedom) the average will be more stable     ( proportionally to  1/sqrt(#deg.of.freedom-3 )  ... moreover the thermal excitations of vibrational modes will be sampled more faithfully.

best

stefano

On 13/04/2018 21:39, Jie Peng wrote:

Dear all


I have been running MD simulations on HfS2 using cp.x code in Quantum espresso. I start from initial configuration obtained from pwscf vc-relax, and relax the system using cp.x by consecutive steps of: electron relaxation->ionic relaxation->cell relaxation. Then, I just directly start a NVE simulation starting from the equilibrium configuration. I expect the system to almost stay stationary or the temperature should be very small since I am allowing dynamics in a system that is already in equilibrium. However, what I see is a huge fluctuation in the /tmpp/ output of cp.x, as I attach a figure showing variation of tmpp (Ionic temperature) with simulation time


I did this because it is suggested in the user guide you should apply an initial displacement to the atoms in your system after the relaxation since otherwise there will not be any dynamics. But what I see here is a large fluctuation of the system temperature.

The thinking or questions here are


1.Does the tmpp represents the physical temperature of the system here? I think it should be since it is the temperature corresponding to kinetic energy of the ions.


2.It above point is true, why is the temperature varying so fiercely? Am I setting incorrect parameters, for instance the timestep or the fictitious mass? But I took those from previous simulation steps where I did the relaxation, and they all worked well since they successfully drived my system to equilibrium, satisfying the convergence threshold on total energy, forces acting on atoms, and the fictitious electron kinetic energy. I am confused at this point.

The input file for NVE simulation is attached here:

/&control/
/    calculation='cp',/
/    title='Halfnium disulfide'/
/    restart_mode='restart',/
/    ndr=53,/
/    ndw=54,/
/    nstep=50000,/
/    iprint=10/
/    isave=100,/
/    tstress = .true./
/    tprnfor = .true./
/    dt=10,/
/    wf_collect=.true./
/    etot_conv_thr=1e-6/
/    forc_conv_thr=1e-3/
/    ekin_conv_thr=1e-5/
/    prefix='HfS2',/
/    pseudo_dir='/home/jpeng/HfS2/potential'/
/    outdir='./tmp/',/
/ //
/ &system/
/    ibrav= 4,/
/    a=3.6529/
/   c=5.6544/
/    nat=  3, ntyp= 2,/
/    ecutwfc =50/
/    vdw_corr='DFT-D',/
/ !   lspinorb=.true./
/ !   noncolin=.true./
/ !   ecutrho=300/
/ !   nbnd=14/
/!    occupations='smearing'/
/!    smearing='gaussian'/
/!   degauss=0.01/
/ !  nspin=2/
/ !   starting_magnetization(1)=0.1/
/! Hf  95.94  Hf.pbe-mt_fhi.UPF/
/! S  32.065  S.pbe-mt_fhi.UPF/
///
/ &electrons/
/    electron_dynamics='verlet'/
/    electron_velocities='zero'/
/    emass=400/
/    emass_cutoff=1/
///
/ &ions/
/    ion_dynamics = 'verlet'/
/    ion_damping=0.1/
/!    ion_nstepe=10/
/ //
/ &cell/
/    cell_dynamics = 'none'/
//
///
/ATOMIC_SPECIES/
/ Hf  95.94  Hf.pbe-mt_fhi.UPF/
/ S  32.065  S.pbe-mt_fhi.UPF/
/ATOMIC_POSITIONS (crystal)/
/Hf      -0.000000000  -0.000000000  -0.000000000/
/S        0.666666667   0.333333333   0.257234636/
/S        0.333333333   0.666666667  -0.257234636/

Anyone could help me on it? Thank you very much.

Best
Jie
--
------------------------------------------------------------------------------------------------------------------------
Jie Peng
PhD student
2134 Glenn Martin Hall, Mechanical Engineering, University of Maryland
College Park, Maryland, USA
Phone:(+1) 240-495-9445
Email: jiep...@umd.edu <mailto:jiep...@umd.edu>

_______________________________________________
users mailing list
users@lists.quantum-espresso.org
https://lists.quantum-espresso.org/mailman/listinfo/users



_______________________________________________
users mailing list
users@lists.quantum-espresso.org
https://lists.quantum-espresso.org/mailman/listinfo/users