My Community

hello everybody:
For my recent research, I need to know the individual force on ion in OUTCAR as following:
Anyone knows the detail of how to calculate the non-local-force and convergence-correction in VASP?and what's it's physical mean?
By the way,I have sum the 4 kind of FORCE(electron-ion +ewald + non-local+convergence-correction)for each atom but it not equal to TOTAL-FORCE ...why?



[align=center][/align]
FORCES acting on ions
electron-ion (+dipol) ewald-force non-local-force convergence-correction
-----------------------------------------------------------------------------------------------
0.188E-13 0.561E-13 0.552E+02 -.140E-17 -.182E-16 -.603E+02 0.000E+00 0.000E+00 0.512E+01 -.190E-14 0.143E-13 0.265E-03
0.955E-13 -.231E-12 -.545E+02 0.137E-16 0.893E-16 0.603E+02 0.000E+00 0.847E-21 -.582E+01 -.132E-13 0.189E-12 0.942E-02
-----------------------------------------------------------------------------------------------
0.114E-12 -.175E-12 0.688E+00 0.123E-16 0.711E-16 0.000E+00 0.000E+00 0.847E-21 -.701E+00 -.151E-13 0.204E-12 0.969E-02


POSITION TOTAL-FORCE (eV/Angst)
-----------------------------------------------------------------------------------
5.00000 5.00000 4.35650 0.000000 0.000000 0.007012
5.00000 5.00000 5.64350 0.000000 0.000000 -0.007012
-----------------------------------------------------------------------------------
total drift: 0.000000 0.000000 -0.004156


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I don't have any knowledge about the evaluation of the non-local-force or the convergence-correction. Regarding the sum of the four forces however, it seems to add up nice. Consider the z-component of the first ion:

(0.552E+02) + (-.603E+02) + (0.512E+01) + (0.265E-03) = 0.020265

This should be compared to 0.007012, so yes there is a 0.013253 difference. However, considering that you don't see additional digits in for example (0.552E+02), this is a good agreement. So if more digits where to be printed you would probably see an exact agreement.

Best regards,
/Dan
<span class='smallblacktext'>[ Edited Wed May 20 2009, 01:55PM ]</span>

Force is the derivative of the total energy with respect to the ionic positions. The derivative of the eigenvalues with respect to the ionic positions can be evaluated by Hellman-Feymann theorem, which is basically calculating the expectation values of the derivative of the Hamiltonian(with respect to ionic positions). The derivative of the Hamiltonian contains terms from the local and non-local part of the ionic pseudopotential. The vasp output prints out the force from these different contributions.

The convergence correction is a correction to the force evaluation due to inaccuracies of self-consistency. You can read the details in PRB 47, 4771 (1993). Since the self-consistency is not exact when you quit the self-consistency loop, there is certain errors in the wave functions, say epsilon. The total energy is a functional of the charge density, therefore it converges pretty fast as epsilon^2. However, the force converges more slowly as epsilon only. The convergence correction is an estimate of this error such that you don't need to do a large number of self-consistent iterations to get an accurate force.