Pullay stress is a corrected stress between the real stress and computed stress (from plane waves) due to imcompleteness of basis sets. It may be non-zero if you allow for simulation box's change (either volumetric or shape-wise). The external pressure are external applied stress which is used to balance the internal stress of simulation box. Pstress is the trace of external stress tensor and can be seen as hydrostatic pressure. If Pstress is positive, external force acting on simulation box is tensile and box is under tension and the internal pressure is negative. If Pstress is negative, external force is compressive and box is under compression and the internal pressure is positive. 

Dear Thao,

Fenglin is correct that the Pulay stress is due to the use of an incomplete basis set. In the case of plane-wave basis sets (e.g. those of ABINIT, Castep, Quantum Espresso, VASP) the incompleteness arises because of the finite number of plane-waves used in the calculation (i.e. the cut-off energy) and the size of the Pulay stress will decrease if you include more plane-waves (i.e. a higher cut-off energy).

Francis and Payne derived an energy and stress correction for this incompleteness (the "finite basis set correction"); for details see:

G P Francis and M C Payne 1990 J. Phys.: Condens. Matter 2 4395 doi:10.1088/0953-8984/2/19/007

or for a brief overview see, for example:

http://www.tcm.phy.cam.ac.uk/castep/documentation/WebHelp/content/modules/castep/thcastepplanebasis.htm

All the best,

Phil Hasnip

 Thank you so much for your answers. 

Hi,

I still do not understand what does "negative external pressure" mean?! Or what does its magnitude show? For example if I have extern.P=-10KB while Pullay.S=0, what does it mean?!

A negative external pressure means the simulation cell is being expanded ("pulled" apart) by the external pressure, whereas a positive one means it is being compressed.

So, this means that if I want to get closer to zero external pressure, I have to increase the cell volume?!

Dear All,

Generally people calculate external pressure on system (when they study high pressure phase change etc.) from E-V data using BIrch-Munaghan equation of state.

What is the difference between pressure from B-M equation and pressure from VASP output file.

Thank You All

Expanding on the previous question:

When I run a simulation with different lattice constants, use the BM state equation to find the cell volume corresponding to minimal energy and then use this cell in a final run, I still get a non-zero external pressure.

In my simulations (4 atom Ni fcc supercell, for example), I get an external pressure close to 0 for a lattice constant that is smaller than that corresponding to the energy minimum.

Can anyone explain why this is the case?

Here are typical INCAR settings:

## --- ENERGY ---

ENMAX=400

ENCUT=520

#

## --- Simulation precision ---

PREC=Accurate

EDIFF=1.e-7

EDIFFG=1.e-6

LREAL=Auto

ROPT=1.e-4

#ISMEAR=-5

ISMEAR=2

SIGMA=0.07