EFIELD PEAD: Difference between revisions

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{{DISPLAYTITLE:EFIELD_PEAD}}
{{TAGDEF|EFIELD_PEAD|[real array]}}
{{TAGDEF|EFIELD_PEAD|[real array]}}
{{DEF|EFIELD_PEAD|3*0.01|if {{TAG|LCALCEPS}}{{=}}.TRUE.|3*0.0|else}}
{{DEF|EFIELD_PEAD|3*0.01|if {{TAG|LCALCEPS}}{{=}}.TRUE.|3*0.0|else}}


Description: {{TAG|EFIELD_PEAD}} specifies the homogeneous electric field in the electric enthalpy functional used to compute the [[Berry_phases_and_finite_electric_fields#Self-consistent_response_to_finite_electric_fields|self-consistent response to finite electric fields]].
Description: {{TAG|EFIELD_PEAD}} specifies the homogeneous electric force field in the electric enthalpy functional used to compute the [[Berry_phases_and_finite_electric_fields#Self-consistent_response_to_finite_electric_fields|self-consistent response to finite electric fields]]. {{TAG|EFIELD_PEAD}} is specified in units of eV/Å.
{{NB|mind| If {{TAG|EFIELD_PEAD}} is used in combination with {{TAG|LCALCEPS}}{{=}}.TRUE., electric field values below 1E-5 will be reset to the default value.}}
----
----
If the {\tt EFIELD\_PEAD} tag is set, VASP will first determine the zero-field
If
groundstate of the system, and subsequently switch on the electric field
{{TAG|EFIELD_PEAD}}=<span style="font-size:16pt">''&epsilon;''</span><sub>x</sub> <span style="font-size:16pt">''&epsilon;''</span><sub>y</sub> <span style="font-size:16pt">''&epsilon;''</span><sub>z</sub>
and compute the field-polarized groundstate orbitals.
 
Additionally, from the change in the macroscopic electronic polarization
is set, with |<span style="font-size:14pt">''&epsilon;''</span>|>0, VASP will first determine the zero-field groundstate of the system, and subsequently switch on the electric field and compute the field-polarized groundstate orbitals.
due to the applied electric field, VASP calculates (part of) the components
 
on the diagonal of the ion-clamped static dielectric tensor ($\epsilon_\infty$),
Additionally, from the change in the macroscopic electronic polarization due to the applied electric field, VASP calculates (part of) the components on the diagonal of the ion-clamped static dielectric tensor (&epsilon;<sub>&infin;</sub>), in accordance with:
in accordance with:
 
\begin{equation}
:<math>
\epsilon^\infty_{ii}=1+
\epsilon^\infty_{ii}=1+
\frac{4\pi}{\epsilon_0}\frac{\partial P_i}{\partial {\mathcal E}_i},
\frac{4\pi}{\epsilon_0}\frac{\partial P_i}{\partial \mathcal{E}_i},
\qquad
\qquad
{i=x,y,z}
{i=x,y,z}
\end{equation}
</math>
 
Beware: this option is only useful if one is interested in selected components on the diagonal of the ion-clamped dielectric tensor (for instance, in cubic systems). To calculate the full ion-clamped dielectric tensor of a system


\noindent
:<math>
Beware: this option is only useful if one is interested in selected
components on the diagonal of the ion-clamped dielectric tensor
(for instance, in cubic systems).
To calculate the full ion-clamped dielectric tensor of a system
\begin{equation}
\epsilon^\infty_{ij}=\delta_{ij}+
\epsilon^\infty_{ij}=\delta_{ij}+
\frac{4\pi}{\epsilon_0}\frac{\partial P_i}{\partial {\mathcal E}_j},
\frac{4\pi}{\epsilon_0}\frac{\partial P_i}{\partial \mathcal{E}_j},
\qquad
\qquad
{i,j=x,y,z}
{i,j=x,y,z}
\end{equation}
</math>
from field-polarized calculations, use {\tt LCALCEPS}=.TRUE.\index{INCAR!L!LCALCEPS|textit}
 
(see Sec.~\ref{incar-lcalceps}).\\
from field-polarized calculations, use {{TAG|LCALCEPS}}=.TRUE..


'''Note''': One should be aware that when the electric field is chosen to be too large, the electric enthalpy functional will lose its minima, and VASP will not be able to find a stationary solution for the field-polarized orbitals.
'''Note''': One should be aware that when the electric field is chosen to be too large, the electric enthalpy functional will lose its minima, and VASP will not be able to find a stationary solution for the field-polarized orbitals.
This is discussed in some detail in~\cite{Berry:pead2}.
This is discussed in some detail by Souza ''et al.''.<ref name="souza:prl:02"/>
VASP will produce a warning if:
VASP will produce a warning if:


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where ''E''<sub>gap</sub> is the bandgap, '''a'''<sub>i</sub> are the lattice vectors, and ''N''<sub>i</sub> is the number of '''k'''-points along the reciprocal lattice vector ''i'', in the regular (''N''<sub>1</sub>&times;''N''<sub>2</sub>&times;''N''<sub>3</sub>) '''k'''-mesh. The factor 1/10 is chosen to be on the safe side. If one does not include unoccupied bands, VASP is obviously not able to determine the bandgap and can not check whether the electric field might be too large. This will also produce a warning message.
where ''E''<sub>gap</sub> is the bandgap, '''a'''<sub>i</sub> are the lattice vectors, and ''N''<sub>i</sub> is the number of '''k'''-points along the reciprocal lattice vector ''i'', in the regular (''N''<sub>1</sub>&times;''N''<sub>2</sub>&times;''N''<sub>3</sub>) '''k'''-mesh. The factor 1/10 is chosen to be on the safe side. If one does not include unoccupied bands, VASP is obviously not able to determine the bandgap and can not check whether the electric field might be too large. This will also produce a warning message.


----
=== An example: &epsilon;<sub>&infin;</sub> in NaF ===
Further aspects of these calculations are more conveniently discussed by means of an example: '''&epsilon;<sub>&infin;</sub> in NaF'''.


*Using the following {{FILE|INCAR}} file:
*Using the following {{FILE|INCAR}} file:
Line 130: Line 128:


----
----
To speed up the computation of the field-polarized groundstate one may set {{TAG|SKIP_EDOTP}}=.TRUE. to avoid the recalculation of the electronic polarization at each iteration during the scf procedure.
To speed up the computation of the field-polarized groundstate one may set {{TAG|SKIP_EDOTP}}=.TRUE. to avoid the recalculation of the [[Berry_phases_and_finite_electric_fields#pol|electronic polarization]] at each iteration during the SCF procedure.
However, the additional term in Hamiltonian (second term on the right-hand-side of [[Berry_phases_and_finite_electric_fields#HdotP|the electric enthalpy functional]]) has to be correctly included and can not be kept fixed.
However, the additional term in Hamiltonian (second term on the right-hand-side of [[Berry_phases_and_finite_electric_fields#HdotP|the electric enthalpy functional]]) has to be correctly included and can not be kept fixed.
Basically this means one does not minimize the total energy but optimizes the orbitals until a stationary point is reached. A stationary point is considered to be reached as soon as the norm of the gradient on the orbitals is smaller than {{TAG|EDIFF}}/100, and the SCF procedure will stop.
Basically this means one does not minimize the total energy but optimizes the orbitals until a stationary point is reached. A stationary point is considered to be reached as soon as the norm of the gradient on the orbitals is smaller than {{TAG|EDIFF}}/100, and the SCF procedure will stop.
Line 150: Line 148:
     1 F= -.29571844E+03 E0= -.29571844E+03  d E =-.223448E-12
     1 F= -.29571844E+03 E0= -.29571844E+03  d E =-.223448E-12


== Related Tags and Sections ==
== Related tags and articles ==
{{TAG|SKIP_EDOTP}},
{{TAG|SKIP_EDOTP}},
{{TAG|LCALCPOL}},
{{TAG|LCALCPOL}},
Line 161: Line 159:
{{TAG|DIPOL}},
{{TAG|DIPOL}},
[[Berry_phases_and_finite_electric_fields|Berry phases and finite electric fields]]
[[Berry_phases_and_finite_electric_fields|Berry phases and finite electric fields]]
{{sc|EFIELD_PEAD|Examples|Examples that use this tag}}
== References ==
<references>
<ref name="souza:prl:02">[http://link.aps.org/doi/10.1103/PhysRevLett.89.117602 I. Souza, J. Íñiguez, and D. Vanderbilt, Phys. Rev. Lett. 89, 117602 (2002).]</ref>
</references>
----
----
[[The_VASP_Manual|Contents]]


[[Category:INCAR]]
[[Category:INCAR tag]][[Category:Linear response]][[Category:Dielectric properties]][[Category:Berry phases]]

Latest revision as of 18:18, 6 July 2023

EFIELD_PEAD = [real array] 

Default: EFIELD_PEAD = 3*0.01 if LCALCEPS=.TRUE.
= 3*0.0 else

Description: EFIELD_PEAD specifies the homogeneous electric force field in the electric enthalpy functional used to compute the self-consistent response to finite electric fields. EFIELD_PEAD is specified in units of eV/Å.

Mind: If EFIELD_PEAD is used in combination with LCALCEPS=.TRUE., electric field values below 1E-5 will be reset to the default value.

If 

EFIELD_PEAD=εx εy εz

is set, with |ε|>0, VASP will first determine the zero-field groundstate of the system, and subsequently switch on the electric field and compute the field-polarized groundstate orbitals.

Additionally, from the change in the macroscopic electronic polarization due to the applied electric field, VASP calculates (part of) the components on the diagonal of the ion-clamped static dielectric tensor (ε∞), in accordance with:

Beware: this option is only useful if one is interested in selected components on the diagonal of the ion-clamped dielectric tensor (for instance, in cubic systems). To calculate the full ion-clamped dielectric tensor of a system

from field-polarized calculations, use LCALCEPS=.TRUE..

Note: One should be aware that when the electric field is chosen to be too large, the electric enthalpy functional will lose its minima, and VASP will not be able to find a stationary solution for the field-polarized orbitals. This is discussed in some detail by Souza et al..[1] VASP will produce a warning if:

where Egap is the bandgap, ai are the lattice vectors, and Ni is the number of k-points along the reciprocal lattice vector i, in the regular (N1×N2×N3) k-mesh. The factor 1/10 is chosen to be on the safe side. If one does not include unoccupied bands, VASP is obviously not able to determine the bandgap and can not check whether the electric field might be too large. This will also produce a warning message.

An example: ε∞ in NaF

  • Using the following INCAR file:
PREC = Med
EDIFF= 1E-6

ISMEAR = 0

EFIELD_PEAD = 0.0 0.0 0.01
The computation of the static dielectric properties from the field-polarized groundstate orbitals requires a very tight convergence of the solutions. The EDIFF-tag specifies the usual convergence criterium for the zero-field solution. As a default VASP will try for an even tighter convergence of the field-polarized groundstate: EDIFF/100! Reaching this level of convergence may be very costly and in rare cases even impossible.
6x6x6
 0
Gamma
 6 6 6
 0 0 0
Note: The PEAD related routines only work for regular meshes of k-points that include the Γ-point, i.e.~either uneven meshes (not recommended) or Γ-centered meshes (like the one above).
NaF
 4.5102
 0.0 0.5 0.5
 0.5 0.0 0.5
 0.5 0.5 0.0
1 1
Direct
  0.0000000000000000  0.0000000000000000  0.0000000000000000
  0.5000000000000000  0.5000000000000000  0.5000000000000000
  • and LDA Na_sv and F PAW datasets.

With the input above, running VASP should produce something akin to: 

 entering main loop
       N       E                     dE             d eps       ncg     rms          rms(c)
DAV:   1    -0.121171874254E+03   -0.12117E+03   -0.11093E+04   392   0.169E+03
DAV:   2    -0.290944564657E+03   -0.16977E+03   -0.15372E+03   412   0.454E+02
DAV:   3    -0.296448270211E+03   -0.55037E+01   -0.54726E+01   516   0.857E+01
DAV:   4    -0.296558918897E+03   -0.11065E+00   -0.11062E+00   432   0.122E+01
DAV:   5    -0.296564115002E+03   -0.51961E-02   -0.51960E-02   568   0.177E+00    0.512E+00
      ...         ...                ...
      ...         ...                ...
DAV:  11    -0.295718441201E+03    0.31316E-05   -0.40516E-06   436   0.471E-02    0.256E-03
DAV:  12    -0.295718441337E+03   -0.13610E-06   -0.13352E-06   276   0.146E-02
       N       E                     dE             d eps       ncg     rms          rms(c)
 gam= 0.000 g(H,U,f)=  0.142E-07 0.000E+00 0.322E-02 ort(H,U,f) = 0.000E+00 0.000E+00 0.000E+00
SDA:   1    -0.295718441659E+03   -0.29572E+03   -0.12885E-02   360   0.322E-02 0.000E+00
      ...         ...                ...
 gam= 0.382 g(H,U,f)=  0.220E-07 0.167E-07 0.186E-10 ort(H,U,f) =-0.260E-08-0.389E-08 0.523E-10
DMP:   4    -0.295718441597E+03    0.43565E-09   -0.14510E-07   360   0.387E-07-0.644E-08
 gam= 0.382 g(H,U,f)=  0.232E-08 0.318E-09 0.166E-11 ort(H,U,f) =-0.471E-08-0.181E-08 0.590E-11
DMP:   5    -0.295718441603E+03   -0.59431E-08   -0.61690E-10   360   0.264E-08-0.651E-08
 final diagonalization
 p_tot=(  0.875E-06  0.875E-06  0.875E-06 )
       N       E                     dE             d eps       ncg     rms          rms(c)
 p_tot=(  0.875E-06  0.875E-06  0.875E-06 )
dp_tot=(  0.000E+00  0.000E+00  0.000E+00 )  diag[e(oo)]=(    ---      ---    1.00000 )
 gam= 0.000 g(H,U,f)=  0.149E-04 0.000E+00 0.000E+00 ort(H,U,f) = 0.000E+00 0.000E+00 0.000E+00
SDA:   1    -0.295718441612E+03   -0.14804E-07   -0.59582E-05   360   0.149E-04 0.000E+00
      ...         ...                ...
      ...         ...                ...
 gam= 0.519 g(H,U,f)=  0.392E-07 0.000E+00 0.000E+00 ort(H,U,f) = 0.919E-08 0.000E+00 0.000E+00
DMP:   9    -0.295718447444E+03   -0.21085E-07   -0.17608E-07   360   0.392E-07 0.919E-08
 p_tot=(  0.868E-06  0.868E-06  0.116E-02 )
dp_tot=( -0.721E-08 -0.723E-08  0.116E-02 )  diag[e(oo)]=(    ---      ---    1.91593 )
 gam= 0.519 g(H,U,f)=  0.210E-07 0.000E+00 0.000E+00 ort(H,U,f) =-0.164E-08 0.000E+00 0.000E+00
DMP:  10    -0.295718447453E+03   -0.83301E-08   -0.80481E-08   360   0.210E-07-0.164E-08
 final diagonalization
 p_tot=(  0.860E-06  0.860E-06  0.118E-02 )
dp_tot=( -0.154E-07 -0.155E-07  0.118E-02 )  diag[e(oo)]=(    ---      ---    1.92723 )
   1 F= -.29571845E+03 E0= -.29571845E+03  d E =-.223452E-12

where one can discern three distinct blocks of SCF iterations. The first one (steps marked with DAV) corresponds to the calculation of the zero-field groundstate. After this groundstate has been reached, the k-point mesh is regenerated using a set of symmetry operations, which takes into account that the symmetry of the system is possibly reduced by the applied electric field. In most cases the new set of k-points is larger than the original one. The orbitals at the additional k-points are generated from their symmetry equivalent counterparts in the zero-field case. This expanded set of orbitals is now reoptimized until convergence is better than EDIFF/100 (the second block, marked DMP), and the initial electronic polarization is computed.

Then the electric field is switched on, and the field-polarized groundstate is calculated. This is the last block of steps marked with DMP. From the change in the electronic dipole moment due to the electric field VASP computes (part of) the components on the diagonal of the ion-clamped static dielectric tensor.

This information is found both in the OUTCAR file and on stdout: 

   diag[e(oo)]=(       ----        ----      1.92723 )

To speed up the computation of the field-polarized groundstate one may set SKIP_EDOTP=.TRUE. to avoid the recalculation of the electronic polarization at each iteration during the SCF procedure. However, the additional term in Hamiltonian (second term on the right-hand-side of the electric enthalpy functional) has to be correctly included and can not be kept fixed. Basically this means one does not minimize the total energy but optimizes the orbitals until a stationary point is reached. A stationary point is considered to be reached as soon as the norm of the gradient on the orbitals is smaller than EDIFF/100, and the SCF procedure will stop. In the case of the previous example this will lead to: 

       N       E                     dE             d eps       ncg     rms          rms(c)
 gam= 0.000 g(H,U,f)=  0.149E-04 0.000E+00 0.000E+00 ort(H,U,f) = 0.000E+00 0.000E+00 0.000E+00
SDA:   1    -0.295718441603E+03   -0.60750E-08   -0.59581E-05   360   0.149E-04 0.000E+00
 gam= 0.519 g(H,U,f)=  0.332E-05 0.000E+00 0.000E+00 ort(H,U,f) = 0.629E-05 0.000E+00 0.000E+00
      ...         ...                ...
      ...         ...                ...
 gam= 0.519 g(H,U,f)=  0.124E-07 0.000E+00 0.000E+00 ort(H,U,f) =-0.141E-08 0.000E+00 0.000E+00
DMP:  11    -0.295718435607E+03    0.13956E-06   -0.46725E-08   360   0.124E-07-0.141E-08
 gam= 0.519 g(H,U,f)=  0.637E-08 0.000E+00 0.000E+00 ort(H,U,f) = 0.218E-10 0.000E+00 0.000E+00
DMP:  12    -0.295718435599E+03    0.78403E-08   -0.25522E-08   360   0.637E-08 0.218E-10
 final diagonalization
 p_tot=(  0.844E-06  0.844E-06  0.117E-02 )
dp_tot=( -0.313E-07 -0.313E-07  0.117E-02 )  diag[e(oo)]=(    ---      ---    1.92478 )
   1 F= -.29571844E+03 E0= -.29571844E+03  d E =-.223448E-12

Related tags and articles

SKIP_EDOTP, LCALCPOL, LCALCEPS, LPEAD, IPEAD, LBERRY, IGPAR, NPPSTR, DIPOL, Berry phases and finite electric fields

Examples that use this tag

References

  1. ↑ I. Souza, J. Íñiguez, and D. Vanderbilt, Phys. Rev. Lett. 89, 117602 (2002).
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