The Wannier-90 interface

Summary

`lmf --w90` — Wannier functions via the Wannier90 library

Sun 26 Jul 17:33:35 BST 2026

Computes the overlap matrices M_mn^{k,b} and the projections A_mn^{k} in the FP-LMTO basis and drives the Wannier90 library to produce maximally-localised Wannier functions.

Use

lmf --nosym --w90~proj=1,0~proj=1,1~win=-15,2.8~nb=4~quit <ext>

Option	Type	Default	Meaning
`proj=ib,l`	int,int	—	Trial orbitals: all `2l+1` partial waves of angular momentum `l` at site `ib`. Repeatable.
`proj=ib,l,m`	int,int,int	—	As above but a single `m`, in Questaal’s real-harmonic order `ilm = l²+l+m+1`. For `l=2`: `m = -2,-1,0,+1,+2` = `xy, yz, 3z²-r², zx, x²-y²`, so with cubic axes t₂g is `m = -2,-1,+1` and e_g is `m = 0,+2`.
`nb=#`	int	all bands	Pass only the lowest `#` bands as `num_bands`. Fewer bands makes disentanglement much cheaper.
`win=#,#`	real,real	whole spectrum	Outer energy window for disentanglement, eV (Wannier90 `dis_win_min`/`dis_win_max`).
`froz=[#,]#`	real[,real]	none	Inner (frozen) window, eV (Wannier90 `dis_froz_max`, plus `dis_froz_min` when two values are given): `froz=max` or `froz=min,max`. States within it are kept exactly. `num_wann` must be at least the number of frozen states at every k.
`spin=#`	int	1	Spin channel to wannierise. One Wannier calculation per run; rerun for the other. Collinear only: with SO=1 the spins are coupled, one run covers both, and `spin=2` is refused.
`nit=#`	int	100	Wannier90 `num_iter`.
`nitd=#`	int	200	Wannier90 `dis_num_iter`.
`l3mx=#`	int	6	Truncation of the Rayleigh expansion of `exp(-i b·r)` in the spheres. Convergence is governed by `\\|b\\|·rmt` (not `lmxa`); 6 is generous.
`gmax=#`	real	`HAM_GMAX`	G cutoff for the envelope plane-wave expansion, a.u.
`dump`	flag	off	Have Wannier90 write `w90.mmn_dump`, `w90.amn_dump`, `w90.eig_dump` and the Wannier90 input file `w90.win_dump` (these must be renamed to remove the `_dump` suffix).
`check`	flag	off	Verify the parity invariant while assembling `Omega`, and report the closure `sum_n \\|M_mn\\|²` band by band.
`bzero`	flag	off	Assemble `M` at `b=0` and report `max\\|M-I\\|`, then stop (see below).
`rand`	flag	off	Replace the projections by random ones.
`quit`	flag	off	Stop after the Wannier functions are made.

num_wann is not an option: it is the length of the projector list (doubled under SO=1; see the spin–orbit section below).

Notes

LMTO basis only.
Collinear and SO=1 (spinor) cases (perturbative SO, SO=3,4, modes are refused).
Full BZ required; run with --nosym.
Atom-centred projections only.
Local orbitals are not handled (the (phi,phidot) pair is taken as complete).

Implementation: src/fp/w90fp.F, called from bndfp.f. Wannier90 is an optional dependency in the manner of libxc/spglib: configure with wannier90[=PATH] (a wannier90 checkout or install prefix, or set WANNIER90_LIB/WANNIER90_INC); without it --w90 reports that lmf was built without the library.

Overlap matrices:

M_mn^{k,b} = <u_mk | u_n,k+b> = M_I + sum_a ( M1_a - M2_a )

M_I — the smooth envelope over the whole cell: a diagonal sum over G (Parseval), no interstitial overlap matrix, no linear solve. G space is necessary, not merely faster: the product of two functions cut off at gmax has content to 2*gmax, which aliases on a mesh.
M1_a, M2_a — true partial waves and their smooth counterparts inside each sphere, via a Rayleigh expansion of exp(-i b·r) and Gaunt contraction. The true waves carry the scalar-relativistic measure (small component and mass correction, as in the Hamiltonian’s own overlap); the envelopes are non-relativistic.

Projections:

The projections use the partial waves themselves as trial orbitals, so the angular integral is delta_LL' and no Gaunt contraction arises:

A_mn = [ conjg(aus_1) + conjg(aus_2)*<phidot|phidot> ] / sqrt(1 + <phidot|phidot>)

Both are phase-free in the sense that no exp(i k·tau) is folded into aus; positions are absolute, which is why M carries an explicit exp(-i 2 pi b·tau_a) and A carries none.

Reference comparisons

Wannier90 tutorials/tutorial02/lead.win

Atom centred s,p given, but use a random initial projection (and more iterations):

ham gmax=5.0
bz nkabc=4
iter conv=1e-7
spec
 atom=Pb z=82 r=3.3
 rsmh= 1.811 2.068 2.2 2.2 eh= -0.1 -0.1 -0.1 -0.1 rsmh2= 1.811 2.068 2.2 eh2= -0.9 -0.9 -0.9
struc nbas=1 alat=4.67775 plat=-1 0 1 0 1 1 -1 1 0
site atom=Pb pos=0 0 0

lmf --nosym --w90~proj=1,0~proj=1,1~nb=8~rand~dump~nit=1000~quit ctrl.pb

Wannier90 tutorials/tutorial03/silicon.win

Frozen window to match the QE run.

bz nkabc=4
ham gmax=8.0
iter nit=25 conv=1e-7
site
  atom=Si xpos=-0.25 0.75 -0.25
  atom=Si xpos=0 0 0
spec atom=Si z=14 r=2.2
  rsmh= 1.492 1.492 1.492 1.492 eh= -0.1 -0.1 -0.1 -0.1 rsmh2= 1.492 1.492 1.492 eh2= -0.9 -0.9 -0.9
struc nbas=2 alat=5.100 plat=-1 0 1 0 1 1 -1 1 0

lmf --nosym --w90~proj=1,0~proj=1,1~nb=12~froz=2.768~dump~quit ctrl.si

Wannier90 tutorials/tutorial04/copper.win

Can’t project on cell-centred s functions; reduce to 5 d-orbitals:

ham autobas[mto=4 lmto=5] gmax=7.0
bz nkabc=4
iter conv=1e-7
spec
  atom=Cu z=29 r=2.412
  rsmh= 1.608 1.608 1 1.608 eh= -0.1 -0.1 -0.1 -0.1 rsmh2= 1.608 1.608 1 eh2= -0.9 -0.9 -0.9
struc nbas=1 alat=3.411 plat=-1 0 1 0 1 1 -1 1 0
site atom=Cu pos=0 0 0

lmf --nosym --w90~proj=1,2~dump~nit=100~quit ctrl.cu

SrTiO3

Require to window disentanglement and provide a frozen (inner) window for e_g states, these are given in eV to options ~win (outer) and ~froz (inner).

ham autobas[mto=14 eh=-0.5] gmax=7.0
bz nkabc=4
iter conv=1e-7 nit=25
struc nbas=5 alat=7.3692 plat=1 0 0 0 1 0 0 0 1
spec
  atom=Sr z=38 r=3.300000 lmx=3 lmxa=5
  atom=Ti z=22 r=2.089716 lmx=3 lmxa=5
  atom=O  z= 8 r=1.594872 lmx=3 lmxa=5
site
  atom=Sr pos= 0.0  0.0  0.0
  atom=Ti pos= 0.5  0.5  0.5
  atom=O  pos= 0.0  0.5  0.5
  atom=O  pos= 0.5  0.0  0.5
  atom=O  pos= 0.5  0.5  0.0

lmf --nosymm --w90~proj=2,2~win=0.0,10.0~froz=0.0,3.0~dump~quit ctrl.sto

yields:

 w90fp: spin 1  Wannier centres (Ang) and spreads (Ang^2)
  1.949806    1.949806    1.949806      1.719016
  1.949806    1.949806    1.949806      1.719027
  1.949806    1.949806    1.949806      1.439655
  1.949806    1.949806    1.949806      1.719020
  1.949806    1.949806    1.949806      1.439833

Running wannier90

the dump option prints the inputs needed to run Wannier90 directly after the lmf run.
rename the files to the expected extensions: # rename "_dump" "" *dump.
run the wannier90 executable via wannier90.x w90.
add different options as needed to the .win file; it is only necessary to rerun lmf if you need to change any of the number of bands, number of wannier functions and choice of projections, or the k-mesh.

for WF band plotting, add a suitable path to the “w90.win” file: Wannier90 expects reduced coordinates while lmf by default uses Cartesian; for cubic STO we are lucky that they are identical:

  bands_plot = .true.
  begin kpoint_path
         X 0.5 0.0 0.0   G 0.0 0.0 0.0
         G 0.0 0.0 0.0   M 0.5 0.5 0.0
         M 0.5 0.5 0.0   R 0.5 0.5 0.5
         R 0.5 0.5 0.5   G 0.0 0.0 0.0
  end kpoint_path

some data manipulation is needed to overlay the bands (see ); some utilities are provided to help this–see the SO=1 section below.

Plotting/overlaying lmf/Wannier90 bands

syml2win: creates Wannier90 input file instructions for reproducing the band plot: it needs the unit cell vectors to order to convert Cartesian to reduced k-points.
wannier2bnds: tabulates the Wannier90 output bands in lmf’s bnds format so that they can be plotted together: it needs $E_F$ from the lmf bnds file, or entered manually: Wannier90 usually doesn’t know/use the Fermi level.
these scripts are available in the utils/ directory.

See the worked example for Pb with SOC below.

Spin–orbit coupling (SO=1)

With HAM SO=1 the spins are coupled (nspc=2): one --w90 run wannierises the full spinor spectrum, with spinors = .true. set in Wannier90 and each M_mn a spinor inner product.

NSPIN=2 is required even without magnetism (the SO token is only read when NSPIN=2); start from zero moments.
Quantisation axis is the global z axis. Each proj= orbital doubles into an (up,down) pair, in that order, so num_wann is twice the length of the projector list. No other axis is available; orient the structure, as with the real-harmonic m selection.
Count in Kramers pairs. Every band is doubly degenerate: choose nb= even. Energy windows (win=, froz=) are safe — exact partners fall on the same side of any edge.

SOC workflow

lmf input for SO=1 case:

    bz nkabc=8
    ham gmax=5.0 nspin=2 so=1
    iter conv=1e-7
    site atom=Pb pos=0 0 0
    spec
     atom=Pb z=82 r=3.3
     rsmh= 1.811 2.068 2.2 2.2 eh= -0.1 -0.1 -0.1 -0.1 rsmh2= 1.811 2.068 2.2 eh2= -0.9 -0.9 -0.9
    struc nbas=1 alat=4.67775 plat=-1 0 1 0 1 1 -1 1 0
    symgrp soc=1

complete command list:

    lmroot=~/kkr-lmto-lapw/lm
    set -e
    set -x

    lmchk --syml ctrl.pb > llmchk

    lmfa ctrl.pb > llmfa

    mpirun -- lmf ctrl.pb > llmf

    mpirun -- lmf --band~fn=syml ctrl.pb > llmf-band

    lmf --nosym --w90~proj=1,0~proj=1,1~nb=8~dump~nit=3000~quit ctrl.pb > llmf-w90

    rename "_dump" "" *dump

    $lmroot/utils/syml2win --plat -1 0 1 0 1 1 -1 1 0 syml.pb >> w90.win

    wannier90.x w90

    $lmroot/utils/wannier2bnds --ef-from bnds.pb w90 > bnds-w90.pb

    band-plot syml.pb bnds.pb:c=grey bnds-w90.pb:c=red -e -15,12 -o pb-bands.pdf

In this case, the WF reliably converge to the mid-cell: they do not stay on the atom centred initial projections (beware that with SO=1, using random initial projections via ~rand may cause the MLWF optimisation to stall in this case).

Result for atom-centred s,p projections:

     Final State
      WF centre and spread    1  (  0.372597, -0.373054,  0.372838 )     2.70562929
      WF centre and spread    2  (  0.372596, -0.373055,  0.372838 )     2.70562929
      WF centre and spread    3  ( -0.373009, -0.372608, -0.372870 )     2.70563805
      WF centre and spread    4  ( -0.373010, -0.372607, -0.372870 )     2.70563805
      WF centre and spread    5  ( -0.372653,  0.373022,  0.372816 )     2.70562780
      WF centre and spread    6  ( -0.372652,  0.373023,  0.372815 )     2.70562780
      WF centre and spread    7  (  0.373064,  0.372640, -0.372785 )     2.70563244
      WF centre and spread    8  (  0.373065,  0.372639, -0.372784 )     2.70563245
      Sum of centres and spreads ( -0.000000, -0.000000, -0.000001 )    21.64505518

             Spreads (Ang^2)       Omega I      =    17.904424328
            ================       Omega D      =     0.010078903
                                   Omega OD     =     3.730551948
        Final Spread (Ang^2)       Omega Total  =    21.645055180

The Wannier interpolated eigenvalues agree well with the original LDA results: in this figure the Wannier WF are plotted in red above the lmf bands in grey: Lead-SOC .