CONQUEST can be used to produce a wide variety of information on the electronic structure of different systems, including: density of states (DOS) and atom-projected DOS (or pDOS); band-resolved charge density; band structure; and electronic polarisation. Many of these are produced with the post-processing <post-proc>
code using a converged charge density <es_conv>
. All of these (at present) require the exact diagonalisation approach to the ground state; linear scaling solutions are not possible.
In most cases (except polarisation <es_pol>
) the data required is produced by a non-self-consistent calculation which reads in a well-converged charge density. The convergence is mainly with respect to Brillouin zone sampling <gs_diag_bz>
, but also self-consistency (a tight tolerance should be used). The basic procedure is:
- Perform a well-converged calculation, writing out charge density (ensure that the Brillouin zone is well sampled, the SCF tolerance is tight (
minE.SCTolerance
) and that the flagIO.DumpChargeDensity T
is set)- Perform a non-self-consistent calculation for the quantity desired (set
minE.SelfConsistent F
andGeneral.LoadRho T
to read and fix the charge density) using an appropriate Brillouin zone sampling- Run the appropriate
post-processing <post-proc>
to generate the data
However, note that the charge density often converges much faster with respect to Brillouin zone sampling than the detailed electronic structure, so the use of a non-self-consistent calculation is more efficient. Often it is most efficient and accurate to use a very high density k-mesh for the final, non-SCF calculation, but a lower density k-mesh to generate the charge density (which converges faster with respect to Brillouin zone sampling than DOS and other quantities).
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The total density of states (DOS) is generated from the file eigenvalues.dat
which is written by all diagonalisation calculations. See density of states <pp_DOS>
for details on parameters which can be set.
The atom-projected DOS resolves the total DOS into contributions from individual atoms using the pseudo-atomic orbitals, and can further decompose this into l-resolved or lm-resolved densities of states. It requires the wave-function coefficients, which will be generated by setting IO.write_proj_DOS T
; further analysis is performed in post-processing <pp_pDOS>
.
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The band structure along a series of lines in reciprocal space can be generated. See post-processing <post-proc>
for more details.
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A band-resolved density is the quantity ∣ ψn(r)∣2 for the nth Kohn-Sham eigenstate (we plot density because the eigenstates are in general complex). It requires wavefunction coefficients which are generated by setting IO.outputWF T
. Full details are found in the band density <pp_band_dens>
section of the post-processing <post-proc>
part of the manual.
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The electronic polarisation (the response of a material to an external electric field) can be calculated using the approach of Resta es-Resta:1992aa
by setting the tag General.CalcPol T
. The direction in which polarisation is found is set using the tag General.PolDir
(choosing 1-3 gives x, y or z, respectively, while choosing 0 gives all three directions, though this is normally not recommended).
The Resta approach is a version of the modern theory of polarisation (MTP) (perhaps better known in the method of King-Smith and Vanderbilt es-KingSmith:1993aa
) where the polarisation is found as:
where L is a simulation cell length along an appropriate direction and V is the simulation cell volume. This approach is only valid in the large simulation cell limit, with Γ point sampling (e.g. for BaTiO3, a minimum of 3x3x3 formula units is needed, though this is perhaps a little too small).
As with all calculations in the MTP, the only valid physical quantity is a change of polarisation between two configurations. A very common quantity to calculate is the Born effective charge (BEC), which is defined as Zk, αβ* = V∂Pα/∂uk, β for species k and Cartesian directions α and β. It is most easily calculated by finding the change in polarisation as one atom (or one set of atoms in a sublattice) is moved a small amount.
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references.bib
Go to top <basissets>
.