Symmetry for magnetic calculation

[kluophysics]

Discussed in https://github.com/deepmodeling/abacus-develop/discussions/5780

^{Originally posted by kluophysics December 29, 2024} I recently tried a system with STRU file

ATOMIC_SPECIES
Mn   54.938  Mn.UPF
Cr   51.996  Cr.UPF
S   32.060  S.UPF

NUMERICAL_ORBITAL
Mn_gga_8au_100Ry_4s2p2d1f.orb
Cr_gga_8au_100Ry_4s2p2d1f.orb
S_gga_7au_100Ry_2s2p1d.orb

LATTICE_CONSTANT
1.889726

LATTICE_VECTORS
0.000000000000  5.059500222100  5.059500222100
5.059500222100  0.000000000000  5.059500222100
5.059500222100  5.059500222100  0.000000000000

ATOMIC_POSITIONS
Direct

Mn
0.000
2
0.000000000000  0.000000000000  0.000000000000  1  1  1  mag  -4.0
0.250000000000  0.250000000000  0.250000000000  1  1  1  mag  -4.0 

Cr
0.000
4
0.625000000000  0.625000000000  0.625000000000  1  1  1  mag  2.0 
0.625000000000  0.625000000000  0.125000000000  1  1  1  mag  2.0
0.625000000000  0.125000000000  0.625000000000  1  1  1  mag  2.0
0.125000000000  0.625000000000  0.625000000000  1  1  1  mag  2.0

S 
0.000
8
0.864000022000  0.864000022000  0.864000022000  1  1  1  mag  0.0 
0.864000022000  0.864000022000  0.407999933000  1  1  1  mag  0.0 
0.864000022000  0.407999933000  0.864000022000  1  1  1  mag  0.0 
0.407999933000  0.864000022000  0.864000022000  1  1  1  mag  0.0 
0.385999978000  0.385999978000  0.842000067000  1  1  1  mag  0.0 
0.385999978000  0.385999978000  0.385999978000  1  1  1  mag  0.0 
0.385999978000  0.842000067000  0.385999978000  1  1  1  mag  0.0 
0.842000067000  0.385999978000  0.385999978000  1  1  1  mag  0.0 

In INPUT I have collinear calculation

nspin                          2
symmetry                       1
noncolin                       0
lspinorb                       0

The ending magnetic moments are

Total Magnetism on atom:  Mn        -4.665702289
Total Magnetism on atom:  Mn        -4.665740501
Total Magnetism on atom:  Cr         2.965500864
Total Magnetism on atom:  Cr         3.022808420
Total Magnetism on atom:  Cr         3.017705694
Total Magnetism on atom:  Cr         3.012714203
Total Magnetism on atom:  S      -0.08423095692
Total Magnetism on atom:  S      -0.08725110486
Total Magnetism on atom:  S      -0.08733743511
Total Magnetism on atom:  S      -0.08678134768
Total Magnetism on atom:  S      -0.08724969023
Total Magnetism on atom:  S      -0.08422655088
Total Magnetism on atom:  S      -0.08733595580
Total Magnetism on atom:  S      -0.08677960017

The magnetic moments of each species are not identical but somewhat close. In contrast, I checked against VASP and QE. Each code (QE and VASP) gives the same magnetic moments for Mn atom and Cr atom (as well as S atom in this case), respectively. Why is it so since symmetry is imposed?

A side note is that the magnetic moments are different from those obtained in VASP and QE. For record,

QE xml output has

       <SiteMagnetization species="Mn" atom="1" charge="12.9155210730199">-3.972369329343096E+000</SiteMagnetization>
        <SiteMagnetization species="Mn" atom="2" charge="12.9155210730200">-3.972369329343080E+000</SiteMagnetization>
        <SiteMagnetization species="Cr" atom="3" charge="11.9087376722326">2.659180873233858E+000</SiteMagnetization>
        <SiteMagnetization species="Cr" atom="4" charge="11.9087376722326">2.659180873233876E+000</SiteMagnetization>
        <SiteMagnetization species="Cr" atom="5" charge="11.9087376722326">2.659180873233858E+000</SiteMagnetization>
        <SiteMagnetization species="Cr" atom="6" charge="11.9087376722326">2.659180873233857E+000</SiteMagnetization>
        <SiteMagnetization species="S" atom="7" charge="4.08901398485960">-9.747697744481396E-002</SiteMagnetization>
        <SiteMagnetization species="S" atom="8" charge="4.08901398421616">-9.747697729427619E-002</SiteMagnetization>
        <SiteMagnetization species="S" atom="9" charge="4.08901398421616">-9.747697729427580E-002</SiteMagnetization>
        <SiteMagnetization species="S" atom="10" charge="4.08901398421616">-9.747697729427582E-002</SiteMagnetization>
        <SiteMagnetization species="S" atom="11" charge="4.08901398421614">-9.747697729427603E-002</SiteMagnetization>
        <SiteMagnetization species="S" atom="12" charge="4.08901398485959">-9.747697744481432E-002</SiteMagnetization>
        <SiteMagnetization species="S" atom="13" charge="4.08901398421614">-9.747697729427580E-002</SiteMagnetization>
        <SiteMagnetization species="S" atom="14" charge="4.08901398421614">-9.747697729427587E-002</SiteMagnetization>

VASP give closer moments, though different from QE and I suspect the pseudopotentials are really different. For QE, I used ONCV of PBE type while the PAW is quite unique. So VASP is not directly comparable, out of the game. For QE and Abacus, both used the same ONCV pseudopotentials and PBE xc functionals, they differ by 0.8 for Mn and 0.4 for Cr. I used DZP basis set and 100 Ry energy cutoff. Hope someone could give me some insight and that would be greatly appreciated!

[mohanchen]

Thanks. @dyzheng @WHUweiqingzhou any thoughts?

[dyzheng]

@kluophysics Hello, how about the k-points after symmetry is on, does ABACUS differ from QE or VASP?

[dyzheng]

I have checked code of symmetry.cpp in ABACUS, it deals with atoms of different non-negative initial magnetisms as same atoms, which is obviously wrong.

[dyzheng]

I will try to fix it, or turn off symmetry analysis for magnetic calculations.

[QuantumMisaka]

@dyzheng This problem may have same origin of #5433

[dyzheng]

@kluophysics Hello，I have tried this case, and I think the result of charge and energy and actually atomic magnetizations with symmetry=1 are same as symmetry=0, but only the atomic magnetizations outcomes are not same, which caused by the mulliken charge calculation method in ABACUS is lack of symmetry.

[dyzheng]

Atomic magnetic momonts:

	symmetry1	symmetry0
Mn1	-4.562569385	-4.562569372
Mn2	-4.562569385	-4.562569372
Cr1	3.225148477	3.248146397
Cr2	3.257748904	3.248146407
Cr3	3.257633478	3.248146407
Cr4	3.252054645	3.248146407
energy	-1232.952219	-1232.952219
total mag	2.00028	2.00028