The effect of an homogeneous static electric field on an insulator may be treated in ABINIT from two perspectives. One is perturbative, and yields the susceptibility in the form of the second derivative of the total energy with respect to the electric field, at zero field strength (see DFPT).
ABINIT can also be used to compute the effect of an electric field of finite amplitude, using techniques from the Modern Theory of Polarization [Resta1994],[Nunes2001],[Souza2002]. The latter is based on the notion of "Berry phase". In this approach, the total energy to minimize includes the contribution due to the interaction of the external electric field with the material polarization PTot, as follows:
E = E0 - ΩPTot.E, where E0 is the usual ground state energy obtained from Kohn-Sham DFT in the absence of the external field E, PTot is the polarization, made up of an ionic contribution and an electronic contribution, and Ω the volume of the unit cell.
Some details of the implementation of The Modern Theory of Polarization in ABINIT are given in [the 2016 ABINIT publication].
In the NCPP case, the electric field has no additional contribution to the Hellmann-Feynman forces, because the electronic states do not depend explicitly on ionic position [Souza2002]. In the PAW case however, as the projectors do depend on ion location, an additional force and additional stresses terms arise [Zwanziger2012].
The generalisation to fixed D-field or fixed reduced fields are also available, as described in M. Stengel, N.A. Spaldin and D. Vanderbilt, Nat. Phys. 5,304 (2009).
The polarization and finite electric field calculation in ABINIT is accessed through the variables berryopt and efield. In addition,
displacement fields and mixed boundary conditions (a mix of electric field and displacement field) can be computed as well.
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Compulsory input variables:
... berryopt [BERRY phase OPTions]
Basic input variables:
... bdberry [BanD limits for BERRY phase]
... dfield [Displacement FIELD]
... efield [Electric FIELD]
... jfielddir [electric/displacement FIELD DIRection]
... kberry [K wavevectors for BERRY phase computation]
... nberry [Number of BERRY phase computations]
Useful input variables:
... berrysav [BERRY SAVe]
... ddamp [electric Displacement field DAMPing parameter]
... maxestep [MAXimum Electric field STEP]
... polcen [POLarization for CENtrosymmetric geometry]
... red_dfield [REDuced Displacement FIELD]
... red_efield [REDuced Electric FIELD]
... red_efieldbar [REDuced Electric FIELD BAR]
Input variables for experts:
... berrystep [BERRY phase : multiple STEP]
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tests/paral/Input: t07.in
tests/v2/Input: t81.in
tests/v4/Input: t55.in t66.in t72.in t75.in t78.in t80.in
tests/v5/Input: t112.in t113.in t23.in
tests/v6/Input: t121.in t122.in t123.in t124.in t125.in t126.in t43.in
tests/v7/Input: t03.in
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