Monopole Dipole and Quadrupole Corrections: Difference between revisions

Revision as of 13:00, 18 October 2023

For charged cells or for calculations of molecules and surfaces with a large dipole moment, the energy converges very slowly with respect to the size $L$ of the supercell. Using methods discussed by Makov et al.^[1] and Neugebauer et al.^[2], VASP can correct for the leading errors (in many details, we have taken a more general approach, though).

Summary of relevant INCAR tags

This section contains a summary of all the INCAR tags that are currently implemented for performing monopole, dipole and quadrupole corrections using VASP. Please see the relevant pages of the respective tags for more detailed information.

Dimensionality of the system	Does the system have net charge?	Does the system have a net dipole moment?	Relevant INCAR tags for monopole/dipole corrections	Do energies converge with cell dimension?
3D	No	No	None	Yes
3D	Yes	No	NELECT: to set the charge LMONO: monopole corrections, only implemented for cubic cells EPSILON: scales monopole correction by dielectric constant of the medium	If the correct EPSILON value is used, the energies and relative energies will not depend on cell size. For solids, see LCALCEPS and LEPSILON
2D	No	Yes	IDIPOL=1,2,3: direction in which to apply the dipole correction to the total energy LDIPOL: enable dipole correction to the potential and forces DIPOL: center of mass to compute the dipole moment	Energies do not depend on the vacuum used (if sufficient vacuum is available)
2D	Yes	No	NELECT: to set the charge	Absolute energies do not converge with cell dimension, but energy differences might be useful
2D	Yes	Yes	NELECT: to set the charge	Absolute energies do not converge with cell dimension, but energy differences might be useful
0D (isolated molecules)	Yes	Yes	NELECT: to set the charge LMONO: monopole corrections, only implemented for cubic cells and only corrects the energy LDIPOL: monopole corrections with corrections for the potentials	Energies do not depend on cell dimension (for large enough cells)
0D (isolated molecules)	Yes	No	NELECT: to set the charge LMONO: monopole corrections, only implemented for cubic cells and only corrects the energy LDIPOL: monopole corrections with corrections for the potentials	Energies do not depend on cell dimension (for large enough cells)
0D (isolated molecules)	No	Yes	LDIPOL: (dipole corrections with corrections for the potentials included)	Energies do not depend on cell dimension (for large enough cells)

Tip: If an external electrostatic field is desired for slab, or molecular calculations, see EFIELD

Current limitations

For the current implementation, there are several restrictions; please read carefully:

Charged systems:

Quadrupole corrections are only correct for cubic supercells (this means that the calculated 1/L³ corrections are wrong for charged supercells if the supercell is non-cubic). In addition, we have found empirically that for charged systems with excess electrons (NELECT>NELECT_neutral) more reliable results can be obtained if the energy after correction of the linear error (1/L) is plotted against 1/L³ to extrapolate results manually for L→∞. This is due to the uncertainties in extracting the quadrupole moment of systems with excess electrons.

Potential corrections are only possible for orthorhombic cells (at least the direction in which the potential is corrected must be orthogonal to the other two directions).

Related Tags and Sections

NELECT, EPSILON, DIPOL, IDIPOL, LDIPOL, LMONO, EFIELD

Examples that use this tag

References

Contents

[Makov95-1] G. Makov and M. C. Payne, Phys. Rev. B 51, 4014 (1995).

[Neugebauer92-2] J. Neugebauer and M. Scheffler, Phys. Rev. B 46, 16067 (1992).

[1]

[2]

@@ Line 1: / Line 1: @@
 For charged cells or for calculations of molecules and surfaces with a large dipole moment, the energy converges very slowly with respect to the size <math>L</math> of the supercell. Using methods discussed by Makov ''et al.''<ref name="Makov95"/> and Neugebauer ''et al.''<ref name="Neugebauer92"/>, VASP can correct for the leading errors (in many details, we have taken a more general approach, though).
-The following flags control the behaviour of VASP:
+== Summary of relevant INCAR tags ==
-* {{TAG|NELECT}}, charged systems:
+This section contains a summary of all the {{FILE|INCAR}} tags that are currently implemented for performing monopole, dipole and quadrupole corrections using VASP. Please see the relevant pages of the respective tags for more detailed information.
-:{{TAG|NELECT}} determines the total number of electrons in the system. The value may deviate from the default value, which is calculated assuming charge neutrality in the system. If {{TAG|NELECT}} differs from the default, an additional neutralizing background charge is applied by VASP. In this case, however, the energy converges very slowly with respect to the size ''L'' of the super cell. The required first order correction to the energy is given by
-::<math>\frac{e^2q^2\alpha}{L\epsilon}</math>
-:where ''q'' is the net charge of the system, &alpha; the Madelung constant of a point charge ''q'' placed in a homogeneous background charge ''-q'', and &epsilon; the dielectric constant of the system. For atoms or molecules surrounded by vacuum, &epsilon; takes on the vacuum value &epsilon;=1. VASP can automatically correct for the leading error, by setting the {{TAG|IDIPOL}} and {{TAG|EPSILON}} tags in the {{FILE|INCAR}} file (see below).
+{|cellpadding="5" cellspacing="0" border="1"
-:It is important to emphasize that the total energy can not be corrected for charged slabs, since a charged slab results in an electrostatic potential that grows linearly with the distance from the slab (corresponding to a fixed electrostatic field). It is fairly simple to show that as a result of the interaction between the charged slab and the compensating background, the total energy depends linearly on the width of the vacuum. Presently, no simple ''a posteriori'' correction scheme is known or implemented in VASP. ''Total energies from charged slab calculations are hence useless, and can not be used to determine relative energies.''
+| Dimensionality of the system
+| Does the system have net charge?
+| Does the system have a net dipole moment?
+| Relevant INCAR tags for monopole/dipole corrections
+| Do energies converge with cell dimension?
+|-
+| 3D
+| No
+| No
+| None
+| Yes
+|-
+| 3D
+| Yes
+| No
+|{{TAG|NELECT}}: to set the charge
+{{TAG|LMONO}}: monopole corrections, only implemented for cubic cells
-:'''Note''': If you are not convinced, simply vary the vacuum width and draw the energy versus the vacuum width.
+{{TAG|EPSILON}}: scales monopole correction by dielectric constant of the medium
+| If the correct {{TAG|EPSILON}} value is used, the energies and relative energies will not depend on cell size. For solids, see {{TAG|LCALCEPS}} and {{TAG|LEPSILON}}
+|-
+| 2D
+| No
+| Yes
+| {{TAG|IDIPOL}}=1,2,3: direction in which to apply the dipole correction to the total energy
+{{TAG|LDIPOL}}: enable dipole correction to the potential and forces
-* {{TAG|EPSILON}}, dielectric constant:
+{{TAG|DIPOL}}: center of mass to compute the dipole moment
-:The {{TAG|EPSILON}}-tag can be used to supply the dielectric constant of the medium. VASP uses this flag only to scale the calculated monopole and dipole corrections. {{TAG|EPSILON}} defaults to 1, which is the proper value for isolated atoms and molcules. For solids, the screening properties can and should be determined using the linear response routines of VASP (see {{TAG|LEPSILON}} and/or {{TAG|LCALCEPS}}). Ionic contributions to the dielectric tensor should be included, if the ions are allowed to relax. Ionic contributions to the dielectric tensor can be calculated using {{TAG|IBRION}}=8.
+| Energies do not depend on the vacuum used (if sufficient vacuum is available)
+|-
+| 2D
+| Yes
+| No
+| {{TAG|NELECT}}: to set the charge
+| Absolute energies do not converge with cell dimension, but energy differences might be useful
+|-
+| 2D
+| Yes
+| Yes
+| {{TAG|NELECT}}: to set the charge
+| Absolute energies do not converge with cell dimension, but energy differences might be useful
+|-
+| 0D (isolated molecules)
+| Yes
+| Yes
+| {{TAG|NELECT}}: to set the charge
+{{TAG|LMONO}}: monopole corrections, only implemented for cubic cells and only corrects the energy
-* {{TAG|IDIPOL}}, type of correction (monopole/dipole and quadrupole):
+{{TAG|LDIPOL}}: monopole corrections with corrections for the potentials
-:For systems with a net dipole moment, the energy converges slowly with respect to the size of the super cell as well. The dipole corrections (and quadrupole corrections for charged systems) fall off like 1/''L''<sup>3</sup>. Both corrections, dipole and quadrupole for charged systems, will be calculated and added to the total energy if {{TAG|IDIPOL}} is set.
+| Energies do not depend on cell dimension (for large enough cells)
+|-
+| 0D (isolated molecules)
+| Yes
+| No
+| {{TAG|NELECT}}: to set the charge
+{{TAG|LMONO}}: monopole corrections, only implemented for cubic cells and only corrects the energy
-:There are four possible settings for {{TAG|IDIPOL}} (= 1 {{!}} 2 {{!}} 3 {{!}} 4).
+{{TAG|LDIPOL}}: monopole corrections with corrections for the potentials
-:For {{TAG|IDIPOL}}=1-3, the dipole moment will be calculated only parallel to the direction of the first, second or third lattice vector, respectively. The corrections for the total energy are calculated as the energy difference between a monopole/dipole and quadrupole in the current supercell and the same dipole placed in a super cell with the corresponding lattice vector approaching infinity. This flag should be used for slab calculations.
+| Energies do not depend on cell dimension (for large enough cells)
-:For {{TAG|IDIPOL}}=4 the full dipole moment in all directions will be calculated, and the corrections to the total energy are calculated as the energy difference between a monopole/dipole/quadrupole in the current supercell and the same monopole/dipole/quadrupole placed in a vacuum, use this flag for calculations for isolated molecules.
+|-
+| 0D (isolated molecules)
+| No
+| Yes
+| {{TAG|LDIPOL}}: (dipole corrections with corrections for the potentials included)
+| Energies do not depend on cell dimension (for large enough cells)
+|}
-:'''Note''': strictly speaking quadrupole corrections is not the proper wording. The relevant quantity is
+{{NB|tip| If an external electrostatic field is desired for slab, or molecular calculations, see {{TAG|EFIELD}}}}
-::<math> \int d^3{\mathbf r} \rho(\mathbf r) \Vert \mathbf r\Vert^2.</math>
-* {{TAG|DIPOL}}, center of the net charge of the cell:
+== Current limitations ==
-:This tag sets the center of the net charge distribution: {{TAG|DIPOL}}='''R'''<sub>center</sub> (in direct coordinates). The dipole is then defined as
-::<math>\int ({\mathbf r}-{\mathbf R}_\mathrm{center})\rho_\mathrm{ions+valence} ({\mathbf r})d{\mathbf r}</math>
-:If {{TAG|DIPOL}} is not set, VASP determines, where the charge density averaged over one plane drops to a minimum and calculates the center of the charge distribution by adding half of the lattice vector perpendicular to the plane where the charge density has a minimum (this is a rather reliable approach for orthorhombic cells).
-* The tag {{TAG|LDIPOL}} enables dipole and if required also monopole corrections to the potential:
-:This tag switch on the potential correction mode. Due to the periodic boundary conditions, not only the total energy converges slowly with respect to the size of the supercell, but also the potential and the forces are affected by finite size errors. This effect can be counterbalanced by setting {{TAG|LDIPOL}}=.TRUE. (dipole corrections) in the {{FILE|INCAR}} file. For {{TAG|LDIPOL}}=.TRUE.,a linear correction and for charged cells  a quadratic electrostatic potential is added to the local potential in order to  correct the errors introduced by the periodic boundary conditions. This is in the spirit of Neugebauer ''et al.''<ref name="Neugebauer92"/> (but more general and the total energy is correctly implemented, whereas the Neugebauer paper contains an erroneous factor 2 in the total energy). The biggest advantage of this mode is that leading errors in the forces are corrected, and that the work-function can be evaluated for asymmetric slabs. The disadvantage is that the convergence to the electronic groundstate might slow down considerably (''i.e.'', more electronic iterations might be required to obtain the required precision). It is recommended to use this mode only after pre-converging the orbitals without the {{TAG|LDIPOL}} flag, and the center of charge should be set in the {{FILE|INCAR}} file ({{TAG|DIPOL}}= center of mass). The user must also ensure that the cell is sufficiently large to determine the dipole moment with sufficient accuracy. If the cell is too small, charge might swap through the vacuum, causing very slow convergence (often convergence improves with the size of the supercell).
-* The {{TAG|LMONO}} switches on monopole corrections for charged systems. The correction is calculated only a posteriori for the total energy. No correction to the potential is calculated.  If corrections for the potential are desired as well, please use the {{TAG|LDIPOL}} instead (for {{TAG|LDIPOL}}=.TRUE., VASP automatically determines whether the system is charged and activates the monopole corrections automatically).
-* {{TAG|EFIELD}}, to apply an electrostatic field:
-:It is possible to apply an external electrostatic field in slab, or molecular calculations. Presently only a single value can be supplied and the field is applied in the direction selected by {{TAG|IDIPOL}}=1-3. The field is supplied in units of eV/&Aring;. Dipole corrections to the potential ({{TAG|LDIPOL}}=.TRUE.) can and should be turned on to avoid interactions between the periodically repeated images.
 For the current implementation, there are several restrictions; please read carefully: