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NEGF calculations converge to unphysical results when 2 leads are different
Date: 2019/08/23 12:14
Name: Maxim Visotin   <visotin.maxim@gmail.com>

Dear all,

My main question is, whether there are any fundamental problems impeding NEGF calculations with two different leads?

I was trying to calculate transmission through a long polyacetylene (CH)_n chain connected to Au nanorods via -S- thiol group. The configuration looks like:
...-Au-Au-Au - S-CH-[CH]n-CH -S - Au-Au-Au-...
(left_lead - central_region - right_lead)

The NEGF calculation of this system works fine and the transmission coefficient energy dependence looks consistent with what is expected from the band structures of the rods and the polyacetylene chain. The results also converge with the length of the CH chain in the central scattering region. Calculation with small bias voltage works fine too.
Unfortunately, subsequent calculations are planned to use even larger Au leads. Larger system will either exceed available RAM or, by reduction of number of processes, take too much computational time.

However, the system has left-right symmetry (inversion center, to be precise), I tried to utilize it and calculate only "half" of the system to reduce computational costs. Thus, I tried the following configuration:
...-Au-Au-Au - S-CH-CH-...

NEGF.bias.voltage was added to compensate the intrinsic difference of the Fermi levels in Au lead and CH lead, so that the resulting bias is zero. The .dat file is copied in the end of the post.

NEGF calculations of this system did converge, but the results look very strange and unphysical. The transmission coefficients are orders of magnitude smaller than in the first case and their energy dependences are different. The spatial distribution of charge (tden) shows that the charge converged to an obviously bad solution: there are abrupt kinks in charge density near the borders of the scattering region (see the picture at https://imgur.com/a/pPiYVCY). There are even negative (-1.28) Mulliken populations at some C atoms.
I have tried to change the mixing schemes and parameters, NEGF.Poisson.Solver, non-equilibrium part integration parameters, basis set, and tried to add more Au layers into the scattering region, but the calculations either converge to the same results or do not converge at all.
Another strange thing is that similar picture is observed if both leads are massive Au nanorods, but of different configurations (I used hexagonal and pentagonal cross-sections) and, thus, different Fermi levels. However, if I reduce the size of the leads, i.e. number of atoms in the cross-section, from ~5-6 to ~3, the artifact suddenly disappears. This gives a hint, that the artifact may be connected to charge mixing in the situation, when the density magnitudes are significantly different across the scattering region.

Is this is a bug or there is some fundamental problem of NEGF calculations with two leads, which differ significantly in densities of states?
Can this be solved via different charge mixing scheme or something else?

Best regards,
Max

P.S. The OpenMX version is 3.8.3 with Mar08,2017 patch including bugfixes of Mixing_DM.c, TRAN_Main_Analysis.c and TRAN_Main_Analysis_NC.c




System.CurrrentDirectory ./ # default=./
System.Name contact_v0__trans
level.of.stdout 1 # default=1 (1-3)
level.of.fileout 1 # default=1 (0-2)

DATA.PATH .. # using basis from previous orbital-optimization runs

#
# Definition of Atomic Species
#
Species.Number 4
<Definition.of.Atomic.Species
Au Au9m-s2p2d1f1 Au_PBE13
H H7.0-s3p2 H_PBE13
C C7.0-s3p3d2 C_PBE13
S S9.0-s4p3d3f2 S_PBE13
Definition.of.Atomic.Species>

#
# Central region
#
Atoms.Number 59
Atoms.SpeciesAndCoordinates.Unit Ang # Ang|AU
<Atoms.SpeciesAndCoordinates
1 Au 12.1234798 16.6329994 -4.1257901 8.5 8.5
2 Au 16.8701802 16.6743202 -4.14954 8.5 8.5
3 Au 18.3818588 12.1723204 -4.1476202 8.5 8.5
4 Au 10.6844597 12.1030102 -4.1178298 8.5 8.5
5 Au 14.5569 9.3438206 -4.1287398 8.5 8.5
6 Au 14.4830904 18.2420998 -4.22612 8.5 8.5
7 Au 19.1312103 14.9317704 -4.2483802 8.5 8.5
8 Au 17.4182301 9.4829998 -4.2232499 8.5 8.5
9 Au 9.8892202 14.8545904 -4.2066202 8.5 8.5
10 Au 11.6932297 9.4223004 -4.2142401 8.5 8.5
11 Au 14.52178 13.3787604 -4.1072002 8.5 8.5
12 Au 14.4936705 15.8894796 -5.6299501 8.5 8.5
13 Au 16.8978004 14.1751099 -5.6440201 8.5 8.5
14 Au 16.0147896 11.3615399 -5.6307802 8.5 8.5
15 Au 12.1231804 14.1353798 -5.6177001 8.5 8.5
16 Au 13.0572596 11.3375597 -5.6196399 8.5 8.5
17 Au 14.52526 13.3800402 -1.20344 8.5 8.5
18 Au 14.50667 15.86343 -2.6534801 8.5 8.5
19 Au 16.8797704 14.1684303 -2.6677499 8.5 8.5
20 Au 15.9974004 11.3884201 -2.6533101 8.5 8.5
21 Au 12.1549997 14.1276798 -2.6441701 8.5 8.5
22 Au 13.0732298 11.3519096 -2.65133 8.5 8.5
23 C 12.94518 12.1812 1.40547 2 2
24 C 12.4256497 11.7904396 2.63198 2 2
25 C 12.8934804 12.2039099 3.89307 2 2
26 C 12.3603697 11.7889796 5.1038899 2 2
27 C 12.8504496 12.2091703 6.3537798 2 2
28 C 12.3428202 11.7981501 7.5781899 2 2
29 C 12.85042 12.2141104 8.8231802 2 2
30 C 12.3542404 11.7979803 10.0492201 2 2
31 H 12.4772196 11.7821799 0.5031801 0.5 0.5
32 H 11.5780096 11.1002302 2.60165 0.5 0.5
33 H 13.7385397 12.8991404 3.91394 0.5 0.5
34 H 11.5153599 11.0927095 5.0921502 0.5 0.5
35 H 13.6967602 12.9042302 6.3538499 0.5 0.5
36 H 11.4976702 11.1018896 7.5801802 0.5 0.5
37 H 13.6959 12.9103004 8.8191405 0.5 0.5
38 H 11.5087996 11.1019602 10.05404 0.5 0.5
39 C 12.8673 12.2111998 11.2954903 2 2
40 C 12.375 11.7935801 12.5195999 2 2
41 H 13.71134 12.9091102 11.2897196 0.5 0.5
42 H 11.5318299 11.0947905 12.52668 0.5 0.5
43 S 14.2725802 13.2475205 1.18152 3 3
44 C 12.3926048 11.7902012 19.9344406 2 2
45 C 12.8921652 12.2104359 18.7077103 2 2
46 C 12.3959723 11.791708 17.46138 2 2
47 C 12.8918172 12.2115059 16.2330895 2 2
48 C 12.3922939 11.7913037 14.9885302 2 2
49 C 12.8870316 12.2101803 13.7594109 2 2
50 C 12.3890209 11.7898236 22.4087601 2 2
51 C 12.8874836 12.2090664 21.1811714 2 2
52 H 11.5553475 11.0837956 19.9320908 0.5 0.5
53 H 13.7293968 12.9169502 18.7098103 0.5 0.5
54 H 11.5591336 11.0847664 17.4608803 0.5 0.5
55 H 13.7286301 12.9184648 16.2314911 0.5 0.5
56 H 11.5553856 11.0842886 14.99148 0.5 0.5
57 H 13.7239247 12.917183 13.7569704 0.5 0.5
58 H 11.5516835 11.0833111 22.4095612 0.5 0.5
59 H 13.7248001 12.9156028 21.1820908 0.5 0.5
Atoms.SpeciesAndCoordinates>
Atoms.UnitVectors.Unit Ang # Ang|AU
<Atoms.UnitVectors
-1.6388 -1.1681 30.70391
25 0 0
0 25 0
Atoms.UnitVectors>



#
# Lead-Left
#
LeftLeadAtoms.Number 48
<LeftLeadAtoms.SpeciesAndCoordinates # Unit=Ang.
1 Au 12.0239867 16.7589305 -7.0428372 8.5 8.5
2 Au 16.9623101 16.800329 -7.0638967 8.5 8.5
3 Au 18.5345873 12.1208083 -7.0665763 8.5 8.5
4 Au 10.5377586 12.0560257 -7.0302145 8.5 8.5
5 Au 14.5592634 9.189218 -7.0412686 8.5 8.5
6 Au 14.4777612 18.3385877 -7.0538982 8.5 8.5
7 Au 19.2255251 14.9603432 -7.077645 8.5 8.5
8 Au 17.4730153 9.3958148 -7.0527919 8.5 8.5
9 Au 9.7957343 14.8807247 -7.0260739 8.5 8.5
10 Au 11.6397564 9.353052 -7.03454 8.5 8.5
11 Au 14.5257467 13.3783019 -7.0501103 8.5 8.5
12 Au 14.493668 15.8894808 -8.4700318 8.5 8.5
13 Au 16.8977962 14.1751117 -8.4840982 8.5 8.5
14 Au 16.0147925 11.361536 -8.4708636 8.5 8.5
15 Au 12.1231831 14.1353829 -8.4577788 8.5 8.5
16 Au 13.0572646 11.3375629 -8.4597192 8.5 8.5
17 Au 12.0239867 16.7589305 -9.9002172 8.5 8.5
18 Au 16.9623101 16.800329 -9.9212767 8.5 8.5
19 Au 18.5345873 12.1208083 -9.9239563 8.5 8.5
20 Au 10.5377586 12.0560257 -9.8875945 8.5 8.5
21 Au 14.5592634 9.189218 -9.8986486 8.5 8.5
22 Au 14.4777612 18.3385877 -9.9112782 8.5 8.5
23 Au 19.2255251 14.9603432 -9.935025 8.5 8.5
24 Au 17.4730153 9.3958148 -9.9101719 8.5 8.5
25 Au 9.7957343 14.8807247 -9.8834539 8.5 8.5
26 Au 11.6397564 9.353052 -9.89192 8.5 8.5
27 Au 14.5257467 13.3783019 -9.9074903 8.5 8.5
28 Au 14.493668 15.8894808 -11.3274118 8.5 8.5
29 Au 16.8977962 14.1751117 -11.3414782 8.5 8.5
30 Au 16.0147925 11.361536 -11.3282436 8.5 8.5
31 Au 12.1231831 14.1353829 -11.3151588 8.5 8.5
32 Au 13.0572646 11.3375629 -11.3170992 8.5 8.5
33 Au 12.0239867 16.7589305 -12.7575972 8.5 8.5
34 Au 16.9623101 16.800329 -12.7786567 8.5 8.5
35 Au 18.5345873 12.1208083 -12.7813363 8.5 8.5
36 Au 10.5377586 12.0560257 -12.7449745 8.5 8.5
37 Au 14.5592634 9.189218 -12.7560286 8.5 8.5
38 Au 14.4777612 18.3385877 -12.7686582 8.5 8.5
39 Au 19.2255251 14.9603432 -12.792405 8.5 8.5
40 Au 17.4730153 9.3958148 -12.7675519 8.5 8.5
41 Au 9.7957343 14.8807247 -12.7408339 8.5 8.5
42 Au 11.6397564 9.353052 -12.7493 8.5 8.5
43 Au 14.5257467 13.3783019 -12.7648703 8.5 8.5
44 Au 14.493668 15.8894808 -14.1847918 8.5 8.5
45 Au 16.8977962 14.1751117 -14.1988582 8.5 8.5
46 Au 16.0147925 11.361536 -14.1856236 8.5 8.5
47 Au 12.1231831 14.1353829 -14.1725388 8.5 8.5
48 Au 13.0572646 11.3375629 -14.1744792 8.5 8.5
LeftLeadAtoms.SpeciesAndCoordinates>


#
# Lead-Right
#
RightLeadAtoms.Number 16
<RightLeadAtoms.SpeciesAndCoordinates # Unit=Ang.
1 C 12.3926048 11.7902012 29.8288613 2 2
2 C 12.8921652 12.2104359 28.6021309 2 2
3 C 12.3959723 11.791708 27.3558006 2 2
4 C 12.8918172 12.2115059 26.1275101 2 2
5 C 12.3922939 11.7913037 24.8829498 2 2
6 C 12.8870316 12.2101803 23.6538315 2 2
7 C 12.3890209 11.7898236 32.3031807 2 2
8 C 12.8874836 12.2090664 31.075592 2 2
9 H 11.5553475 11.0837956 29.8265114 0.5 0.5
10 H 13.7293968 12.9169502 28.604229 0.5 0.5
11 H 11.5591336 11.0847664 27.3553009 0.5 0.5
12 H 13.7286301 12.9184648 26.1259117 0.5 0.5
13 H 11.5553856 11.0842886 24.8858986 0.5 0.5
14 H 13.7239247 12.917183 23.6513901 0.5 0.5
15 H 11.5516835 11.0833111 32.3039818 0.5 0.5
16 H 13.7248001 12.9156028 31.0765114 0.5 0.5
RightLeadAtoms.SpeciesAndCoordinates>



#
# SCF or Electronic System
#
scf.XcType GGA-PBE # LDA|LSDA-CA|LSDA-PW|GGA-PBE
scf.SpinPolarization off # On|Off|NC
scf.ElectronicTemperature 300.0 # default=300 (K)
scf.energycutoff 200.0 # default=150 (Ry)
scf.maxIter 500 # default=40
scf.EigenvalueSolver NEGF # DC|GDC|Cluster|Band
scf.Kgrid 5 1 1 # means n1 x n2 x n3
scf.Mixing.Type rmm-diisk # Simple|Rmm-Diis|Gr-Pulay|Kerker|Rmm-Diisk
scf.Init.Mixing.Weight 0.30 # default=0.30
scf.Min.Mixing.Weight 0.001 # default=0.001
scf.Max.Mixing.Weight 0.300 # default=0.40
scf.Mixing.History 35 # default=5
scf.Mixing.StartPulay 70 # default=6
scf.Kerker.factor 15.0 # default=1

scf.criterion 1.0e-6 # default=1.0e-6 (Hartree)
scf.lapack.dste dstevx # dstevx|dstedc|dstegr.default=dstevx


MD.Type nomd # Nomd|Opt|NVE|NVT_VS|NVT_NH


NEGF.filename.hks.l leads.hks
NEGF.filename.hks.r lead_x4.hks


NEGF.bias.voltage -1.1833 # compensating intrinsic fermi level difference


NEGF.tran.Analysis on # default on
NEGF.tran.Channel on # default on
NEGF.tran.CurrentDensity on # default on
NEGF.tran.energyrange -5 5 1.0e-3 # default=-10.0 10.0 1.0e-3 (eV)
NEGF.tran.energydiv 1000 # default=200
NEGF.tran.Kgrid 1 1 # default= 1 1
NEGF.scf.Iter.Band 35
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Re: NEGF calculations converge to unphysical results when 2 leads are different ( No.1 )
Date: 2019/09/02 16:08
Name: Maxim Visotin  <visotin.maxim@gmail.com>

Dear all,

I think I have an idea of what is going on. If the left and the right sides of the scattering region are different, the first band-SCF steps, which are calculating density distribution for an assumed periodic cell containing the scattering region, will produce very bad charges for the atoms at the borders. These charges are used as a first guess for NEGF charge and is obviously misleading the subsequent charge mixing iterations away from the solution. The problem is the same as what is described as the "local trap" in ordinary NEGF calculations. With a slight difference that the "Band" eigensolver makes situation even worse than initial superposition of atomic charges.

I have tried do some calculations with NEGF.scf.Iter.Band==0 and, despite I haven't obtained convergence (NormRD ~=0.01), the results after 500 iterations show more appropriate charge distribution and Mulliken populations, and the transmission coefficients are of the same order as needed.

If this is the root of the problem, the use of "Cluster" eigensolver for pre-convergence may give better results. Is it technically possible to check it?

Best regards,
Max
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