EFOR
EFOR = [real array]
| Default: EFOR | = 3 * NIONS * 0.0 |
Description: EFOR sets external forces in eV/Å on each atom in the cartesian x-, y-, and z-directions. The order of the ions is equivalent to the order in the POSCAR file, and for each ion, x-, y-, and z-components have to be given.
| Mind: This tag is only available as of VASP.6.5.0. |
The array of external forces will be added to the forces computed internally for each ionic step (ionic minimization or molecular dynamics). If an ionic minimization is performed with non-zero external forces, the converged structures will be only at a minimum accounting for the constraint of the external forces. Regardless of whether the convergence criterion is set to minimize total forces, or converge the total energy.
| Warning: The sum of all external forces set with EFOR must be 0 to avoid drift. |
While the total sum of all external forces in all directions must be zero, it is possible to achieve this by putting balancing forces on an ion that is fixed by the selective dynamics feature in the POSCAR file.
Format
EFOR can be a very long array, as 3 values need to be set for each ion in the system. The format is equivalent to setting the magnetic moments in the noncollinear case using MAGMOM, so it is possible to use an N*F syntax to indicate that the next N entries in the array should be of value F. E.g.:
EFOR = 2*0.0 1.0 188*0.0 -1.0
In this example, we have 64 ions, so we have to set 3*64=192 values in the array. Only the cartesian z components of the first and last ion should be non-zero, which enables a compact INCAR line.
If more force components are non-zero, readability is increased by utilizing the multi-line option in the INCAR file. This is achieved by using backslashes (\) to negate line breaks or put the multi-line expression in quotes ("). E.g. for a 32 atom system with forces in the x- and z-directions on the first and last 8 atoms:
EFOR = "2.0 0.0 1.0 2.0 0.0 1.0 2.0 0.0 1.0 2.0 0.0 1.0 0.0 0.0 1.0 0.0 0.0 1.0 0.0 0.0 1.0 0.0 0.0 1.0 48*0.0 -1.0 0.0 -1.0 -1.0 0.0 -1.0 -1.0 0.0 -1.0 -1.0 0.0 -1.0 -1.0 0.0 -1.0 -1.0 0.0 -1.0 -1.0 0.0 -1.0 -1.0 0.0 -1.0"
Symmetry and periodic boundary conditions
Symmetry considerations
Setting external forces will, in most cases, break some symmetries of the system, resulting in more irreducible k points and thus increased computational effort.
If any non-zero external forces are set, the symmetry reduction is reported in the OUTCAR after all other symmetry operations. E.g.:
Analysis of structural, dynamic, and magnetic symmetry & ext. forces: ===================================================================== Subroutine PRICEL returns: Original cell was already a primitive cell. Routine SETGRP: Setting up the symmetry group for a hexagonal supercell. Subroutine GETGRP returns: Found 6 space group operations (whereof 6 operations were pure point group operations) out of a pool of 24 trial point group operations. The overall configuration with ext. forces has the point symmetry S_6 . Periodic boundary conditions apply in all VASP calculations.
Periodic boundary conditions
All VASP calculations are performed under periodic boundary conditions. When external forces are applied to bulk systems, this can lead to unexpected results. E.g. pushing an atom towards another atom in the same unit cell might pull it further away from the same atom in a neighboring unit cell. Thus external forces cannot be used to uniformly compress or strain a bulk system along a specific axis. This can however be achieved by lengthening or shortening the relevant lattice vector.
On the other hand, external forces should be used if strain needs to be applied to a slab, a molecule, or any other system in which a vacuum region is used. When e.g. a surface slab needs to be compressed in the direction normal to the surface plane, the lattice vector cannot be shortened because this would collapse the vacuum. External forces on the atoms at the surfaces can achieve the desired effect.
| Tip: External forces are typically only used if there is a vacuum region in the simulation cell. |
External forces during on-the-fly learning
External forces can be used during on-the-fly training for machine-learned force fields. In that case, the external forces will be only used during the ionic updates but will be removed for the training. This ensures that only forces arising from interatomic interactions will contribute to the force field and the resulting force field can be used without, or with different external forces.
Output
The external forces are printed to the OUTCAR file after the positions of ions. E.g.:
external forces on ions in cartesian coordinates (eV/Angst): 0.00000000 0.00000000 0.50000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 -0.50000000
After each ionic step, the external forces are included in the reported TOTAL-FORCE array, but not separately listed, since they are not updated during a VASP run.:
POSITION TOTAL-FORCE (eV/Angst)
-----------------------------------------------------------------------------------
-0.00000 -0.00000 20.27571 0.000000 0.000000 0.001257
1.43189 0.82670 22.42983 -0.000000 -0.000000 -0.008077
2.86378 1.65341 24.58497 0.000000 0.000000 0.008077
0.00000 0.00000 26.73909 -0.000000 -0.000000 -0.001257
-----------------------------------------------------------------------------------
total drift: 0.000000 -0.000000 -0.000000
Example
As an example, the compression of an Al(001) slab under 4 GPa of pressure is chosen. At ~39500 times the atmospheric pressure at sea level, this is considerable, but pressures in diamond anvil cells can be two orders of magnitude larger. The four-layer thick slab corresponding to the following POSCAR is already relaxed without external forces:
Al 001 slab
1.00000000000000
4.0472922325000000 0.0000000000000000 0.0000000000000000
0.0000000000000000 4.0472922325000000 0.0000000000000000
0.0000000000000000 0.0000000000000000 16.0709387330000000
Al
8
Selective dynamics
Direct
0.0000000000000000 0.0000000000000000 0.0000000000000000 F F F
0.4999999999382325 0.4999999999382325 0.0000000000000000 F F F
0.0000000000000000 0.4999999999382325 0.1291914423155097 T T T
0.4999999999382325 -0.0000000000000000 0.1291914423155097 T T T
0.0000000000000000 0.0000000000000000 0.2574944356749768 T T T
0.4999999999382325 0.4999999999382325 0.2574944356749768 T T T
0.0000000000000000 0.4999999999382325 0.3864211449750742 T T T
0.4999999999382325 0.0000000000000000 0.3864211449750742 T T T
The pressure has to be converted into the correct units. Forces in VASP are given in eV/Å, and an area in Å2, thus GPa needs to be converted to (eV/Å)/Å2, or eV Å-3:
With a lattice parameter of 4.047Å, the surface area A of the slab is about 16.381 Å2. Thus the total force in eV/Å we have to put on the top layer to compress the slab with 4 GPa of pressure is:
or 0.20448 eV/Å per surface atom. The INCAR file can now be written:
ENCUT = 250 ISMEAR = 1 SIGMA = 0.1 NELMIN = 4 NSW = 60 ISIF = 2 IBRION = 1 POTIM = 0.75 EDIFFG = -0.01 EDIFF = 1E-6 EFOR = 2*0 0.40896 17*0 -0.20448 2*0 -0.20448
Note that the forces on the top atoms are balanced by putting the opposing force on one atom only. This is feasible since both atoms in the bottom layer are fixed by selective dynamics flags.
Using a 5x5x1 Γ-centered mesh in the KPOINTS file, and the standard PBE Al POTCAR, the calculation converges in less than 10 ionic steps.
The slab is compressed by less than 2%, from 6.21 Å to 6.10 Å. This relatively small compression at relatively high pressure is due to three factors:
- 4 GPa corresponds to forces of ~0.2 eV/Å, which is only 20 times the negligible force limit of 0.01 eV/Å in this calculation.
- We do not allow the material to expand in the direction normal to the pressure by keeping the cell shape fixed with ISIF = 2.
- Intra-atomic forces in perfect close-packed metallic crystals are powerful, and lattice imperfections usually mediate deformations in real materials.
For layered materials, molecules on surfaces, and other, less strongly-bound systems, similar forces will have larger effects, however.