Wannier90: Band Structures, Tips and Tricks

J. M. Skelton
University of Bath, UK
WMD [Virtual] Group Meeting
31st October 2016
Wannier90:
Band Structures, Tips and Tricks

Wannier90: Band Structures, Tips and Tricks | Slide 2
Overview
 Wannier90 is a code for obtaining and performing calculations with maximally-localised
Wannier functions
 Comes as a standalone executable, or as a library that can be interfaced with a number of
DFT codes including VASP
 Between wannier90.x and postw90.x, a large number of electronic-structure-
related calculations can be done:
o High-resolution band structures and electronic DoS curves
o Generating band energies at lists of arbitrary k-points (geninterp)
o Berry-curvature (berry) and Boltzmann transport (BoltzWann) calculations
 If we are only interested in electronic-structure calculations, Wannier90 is fairly easy to
use, and you can follow a simple “recipe” to do these calculations

Building VASP with Wannier90 support
 Download Wannier90 1.2 from http://www.wannier.org/download.html [N.B. the
interface from VASP 5.4.1 does not use the latest version]
 For more recent Intel compilers, copy config/make.sys.ifort to make.sys and edit as
follows:
LIBDIR = /opt/intel/mkl721/lib/32
LIBS = -L$(LIBDIR) -lmkl_lapack -lmkl_ia32 -lguide -lpthread
LIBDIR = ${MKLROOT}/lib/intel64
LIBS = -L$(LIBDIR) -mkl -lpthread
 Build the executable and library, run the tests, and check the report:
make wannier lib test

Building VASP with Wannier90 support
 For VASP 5.4.1 and the Intel compilers, edit makefile.include as follows:
CPP_OPTIONS = ...
...
LLIBS = $(SCALAPACK) $(LAPACK) $(BLAS)
CPP_OPTIONS = -DVASP2WANNIER90 ...
...
LLIBS = install_path/libwannier.a $(SCALAPACK) $(LAPACK) $(BLAS)
 (Re)compile VASP:
make veryclean ; make gam std ncl
 N.B. The build was done from a copy of the source with all the latest patches applied - if
you run into any strange build errors, try applying these to see if it fixes it

Building Wannier90 2.0.1
 Download Wannier90 2.0.1 from http://www.wannier.org/download.html
 As before, copy config/make.sys.ifort to make.sys, and this time change the
LIBDIR variable in the section for the Intel MKL libraries:
LIBDIR = /opt/intel/mkl/lib/intel64
LIBDIR = ${MKLROOT}/lib/intel64
 Build the executables and library:
make all
 The make.sys.ifort input file seems to have been written for Intel MPI and so sets
MPIF90=mpiifort; if you are using OpenMPI, you may need to change this to e.g.
mpif90

Our example system: SnS2
 Cell shape/volume fixed to experimental values,1 and atom positions relaxed w/ PBEsol-D3
 Initial setup is the Sn_d and S PAW PPs (26 electrons), 550 eV cutoff, Γ-centered 12x12x8
k-point grid, PREC = Accurate, LREAL = .FALSE. and LASPH = .TRUE.
 All these examples were run on chpc-cobalt (VASP 5.4.1, 32 cores, 128 Gb RAM)
 A set of input files and reference output files can be downloaded from GitHub:
https://github.com/JMSkelton/VASP-Examples/tree/master/Wannier90_SnS2

VASP and Wannier90 workflow
Electronic-Structure Calculation
VASP-to-Wannier90
(LWANNIER90)
Minimise WF Spread
(wannier90.x)
Post-Processing
(wannier90.x/postw90.x)
These two steps can be done separately (in most
cases), or can be combined - see next slide
The convergence of the Wannier interpolation
w.r.t. the WF spread is definitely not intuitive ->
safest to verify your setup by comparing cheap
(e.g. GGA) band structures from VASP and
Wannier90
postw90.x is not included in Wannier90 1.2,
but you can use the v1.2 output in v2.0

The VASP-to-Wannier90 interface
 There are three potential issues with the current Wannier90 interface:
o Calculations with LWANNIER90 fail for NPAR != Default (but KPAR works)
o If there are any errors in the input file, VASP will crash before writing the WAVECAR
file
o Performing the initial projections to generate the Wannier90 input files takes a
very long time, particularly with large NBANDS
 If your calculation saves a WAVECAR file [some flavours of the GW algorithms do not],
there is a filthy hack possible workaround:
1. Perform an electronic-structure calculation and save the WAVECAR
2. Copy the input files + WAVECAR to a workstation, and re-run VASP with
LWANNIER90 = .TRUE., ALGO = None and NELMIN = 0
o N.B. WAVECARs are binary files [I think!], so the HPC and workstation probably
need to use a similar CPU architecture for this to work

Example INCAR for LWANNIER90: Example skeleton wannier90.win file:
Other required tags are added automatically
by VASP:
• num_wann (= NBANDS)
• unit_cell_cart
• atoms_cart
• mp_grid
• kpoints
ALGO = Normal ! None
EDIFF = 1E-8
ENCUT = 550
GGA = PE
ISIF = 2
ISMEAR = -5
KPAR = 8
LASPH = .TRUE.
LREAL = .FALSE.
NBANDS = 64
NELMIN = 5 ! 0
!NPAR = 1
NSW = 0
PREC = Accurate
SYSTEM = SnS2
LWANNIER90 = .TRUE.
Begin Projections
Random
End Projections

Wannier90 band structures
 num_wannier must be set to num_bands
o The W90 band structure will contain num_wannier bands...
o ... so if num_wannier < num_bands, the band structure cannot be accurately
represented
 Since we aren’t interested in the WFs themselves, Random initial projections are fine
 Not specifying an initial projection and setting use_bloch_phases seems to
generate nonsense
 When num_wannier = num_bands, no disentanglement is required, which means
these parameters can be safely ignored
 The only remaining issue is then the convergence of the “Wannierisation” procedure, i.e.
minimising the quadratic spread of the WFs

Begin Projections
Random
End Projections
bands_plot = .true.
bands_plot_format = 'gnuplot'
bands_num_points = 51
begin kpoint_path
G 0.000000 0.000000 0.000000 A 0.000000 0.000000 0.500000
A 0.000000 0.000000 0.500000 H 0.333333 0.333333 0.500000
...
L 0.500000 0.000000 0.500000 H 0.333333 0.333333 0.500000
end kpoint_path
A skeleton wannier90.win file can specify
projections, or VASP will automatically add
use_bloch_phases = T for you
As noted above, other required tags are added
automatically by VASP
This is the number of k-points along the first
segment; the number along the rest will be
adjusted to maintain the same density

Converging the “Wannierisation”
 A number of tags in Wannier90 control the convergence of the “Wannierisation”
procedure:
o num_iter : (maximum) number of minimisations; default = 100
o conv_tol : break criterion on the change in the quadratic spread, ΔΩ 𝐓𝐨𝐭; default =
10-10
o conv_window : number of iterations over which ΔΩ 𝐓𝐨𝐭 must be < conv_tol;
default = -1
 The code only applies conv_tol if conv_window > 1 (remember - the default value is
-1)
o This means increasing num_iter without setting conv_window and/or
conv_tol might be a waste of time (!)
 The minimisation routine is fairly slow, and for most systems [at least, in my experience],
reaching ΔΩ 𝐓𝐨𝐭 < 10-10 on a typical spread of approx. 102 Å2 can take a very long time

Conv. Crit. # Iter t [min] Ω 𝐓𝐨𝐭 [Å2] ΔΩ 𝐓𝐨𝐭 [Å2]
- 0 0.27 558.77 -
- 1 0.30 469.79 -0.88 x 102
- 10 0.51 333.25 -0.66 x 101
- 100 2.81 265.23 -0.54 x 10-1
- 1000 25.83 254.74 -0.19 x 10-2
ΔΩ 𝐓𝐨𝐭 < 1 28 0.96 290.79 -0.97 x 10-1
ΔΩ 𝐓𝐨𝐭 < 10-1 29 1.00 290.75 -0.38 x 10-1
ΔΩ 𝐓𝐨𝐭 < 10-2 172 4.73 259.60 -0.95 x 10-2
ΔΩ 𝐓𝐨𝐭 < 10-3 266 7.52 258.44 -0.85 x 10-3
ΔΩ 𝐓𝐨𝐭 < 10-4 674 17.49 255.23 -0.32 x 10-4
(!)
(!)
(!)
(!)

DoS calculations with postw90
 Once the initial “Wannierisation” has been performed, the converged WFs are stored in
wannier90.chk and can be read by postw90.x
 Using postw90.x to generate a DoS is as simple as adding the relevant tags to
wannier90.win and running e.g. mpirun -np 32 postw90.x wannier90
kmesh = 32 32 24
adpt_smr = .true.
smr_type = 'gauss'
dos = .true.
dos_task = 'dos_plot'
Run the dos module; dos_plot is the
only dos_task currently available
Adaptive smearing: 𝜂 𝑛𝐤 = α 𝛻𝐤 𝜀 𝑛𝐤 Δ𝑘
Size if the k-point mesh - crank it up with
impunity (!)

PBE: final result
531 points/band 32x32x24 mesh

A few more convergence tests...
Pseudopotential LOOP [s]
Sn_d 2.13
Sn 1.67

ENCUT [eV] LOOP [s]
300 1.12
350 1.24
400 1.30
450 1.83
500 2.06
550 2.13

k-Point Mesh LOOP [s]
6x6x5 0.87
7x7x5 0.89
6x6x6 0.99
7x7x6 1.03
8x8x6 2.13

Convergence tests: final result

HSE06 calculations with Wannier90
 HSE06 calculations save WAVECAR files, so we can use the “trick” and do the calculation
in two parts to take advantage of NPAR
ALGO = All
EDIFF = 1E-8
ENCUT = 400
GGA = PE
HFSCREEN = 0.2
KPAR = 4
LHFCALC = .TRUE.
NBANDS = 64
NPAR = 1
NSW = 0
ALGO = None
EDIFF = 1E-8
ENCUT = 400
GGA = PE
HFSCREEN = 0.2
KPAR = 4
LHFCALC = .TRUE.
NBANDS = 64
NELMIN = 0
!NPAR = 1
NSW = 0
LWANNIER90 = .TRUE.
N.B. These INCARs are both
incomplete - see GitHub for full
input files

GW calculations with Wannier90
ALGO = Exact
EDIFF = 1E-8
ENCUT = 400
GGA = PE
ISIF = 2
ISMEAR = -5
KPAR = 4
LASPH = .TRUE.
LOPTICS = .TRUE.
LREAL = .FALSE.
NBANDS = 64
NELMIN = 5
NPAR = 1
NSW = 0
PREC = Accurate
SYSTEM = SnS2
ALGO = GW0 | scGW0 | scGW
EDIFF = 1E-8
ENCUT = 400
GGA = PE
ISIF = 2
ISMEAR = -5
KPAR = 8
LASPH = .TRUE.
LREAL = .FALSE.
NBANDS = 64
NELM = 4 !NELMIN = 5
!NPAR = 1
NSW = 0
PREC = Accurate
SYSTEM = SnS2
LWANNIER90 = .TRUE.
Create and save
WAVEDER file
Ensures converged
conduction bands
Apparently PBE gives
best W0 for GW
Run GW and LWANNIER90
in the same calculation
Can’t use NPAR -> bump
up KPAR instead
Set number of GW
iterations
Five GW ALGOs to
choose from (!)

PBE vs. HSE06 vs. GW: final result

PBE vs. HSE06 vs. GW: final result
Method Eg,dir [eV] Eg,indir [eV]
Expt.1 2.38-2.56 2.25-2.48
PBE 1.915 1.505
HSE06 2.784 2.399
G0W0 2.927 2.517
scGW0 3.109 2.706
scGW 3.335 2.897
1L. A. Burton et al., J. Mat. Chem. A 4, 1312-1318 (2016)

Method t [min]
PBE 2.08
HSE06 156
G0W0 20.6
scGW0 (4 iter.) 153
scGW (4 iter.) 152
PBE vs. HSE06 vs. GW: execution times

Summary
 If all you want from Wannier90 is to interpolate the electronic structure, the “recipe”
outlined here is fairly reliable [in my limited experience (!)]
 Convergence (= minimisation of the WF spread) is not intuitive
o Probably the best advice here is to check your Wannier90 setup is working with a
cheap (e.g. GGA) band structure
 Between wannier90.x and postw90.x, you can do some neat stuff:
o High-resolution band structures + easy modification of band paths
o DoS calculations with fine k-point meshes + eigenvalues at arbitrary lists of k-points
o Several other modules in postw90.x (e.g. berry, BoltzWann)
 If you plan to do an expensive electronic-structure calculation, checking whether the band
energies are converged with a lower plane-wave cutoff and/or k-point sampling than your
default setup could save you a lot of computer time...!

Wannier90: Band Structures, Tips and Tricks

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