Unconventioanl Materials/Obstructed atomic limits （Unconv. Mat.）

• Website: http://tm.iphy.ac.cn/UnconvMat.html
  Refs: J. Gao, et al. "Unconventional materials: the mismatch between electronic charge centers and atomic positions" , Sci. Bul. 67(6), 598-608 (2022) https://doi.org/10.1016/j.scib.2021.12.025
  S. Nie, et al. "Application of topological quantum chemistry in electrides", Phys. Rev. B 103, 205133 (2021).
  S. Nie, et al. "Six-fold Excitations in Electrides", Phys. Rev. Research 3, L012028 (2021).

1. Standardize the POSCAR and generate the aBRs (e.g. Ca2N)

$$ phonopy --tolerance 0.01 --symmetry -c POSCAR > phonopy.out

$$ pos2aBR > aBR.out (converting PPOSCAR to POSCAR_std)

--aBR.out--

   166 R-3m
The matrix Kc2p
  0.666667   -0.333333   -0.333333
  0.333333    0.333333   -0.666667
  0.333333    0.333333    0.333333
The matrix p2cR
   1.000000    0.000000    1.000000
  -1.000000    1.000000    1.000000
   0.000000   -1.000000    1.000000
Origin shift
0.000000    0.000000    0.000000
\\
 SN  Mult. Wyck. Atom  s    p    d  Wyck. Name
   1    2    7   20    2    6    0    6c   Ca
   2    1    9    7    2    3    0    3a   N
\\
 SN  Orb. @ Site     Symm.
  1  Ca-s @ 6c( 7)    3m(19) >>>   BCS  Int. Sch.      Basis
                                1  GM1 ;GM1 ; A1 ;     z;x2+y2;z2
  1  Ca-p @ 6c( 7)    3m(19) >>>   BCS  Int. Sch.      Basis
                                1  GM1 ;GM1 ; A1 ;     z;x2+y2;z2
                                3  GM3 ;GM3 ; E  ;     x,y;xz,yz;x2-y2,xy;Jx,Jy
  2   N-s @ 3a( 9)   -3m(20) >>>   BCS  Int. Sch.      Basis
                                1  GM1+;GM1+; A1g;     x2+y2;z2
  2   N-p @ 3a( 9)   -3m(20) >>>   BCS  Int. Sch.      Basis
                                4  GM2-;GM2-; A2u;     z
                                6  GM3-;GM3-; Eu ;     x,y

2. Run scf and band calculations in VASP for maximial High-symmetry k-points (HSKPs)

(POTCAR: PAW_PBE Ca_sv 06Sep2000; PAW_PBE N 08Apr2002)

$$ cp POSCAR_std POSCAR; run VASP

$$ irvsp2 -sg 166 -nb 9 13 > outir2 (* generating tqc.txt and tqc.data when using only maximal HSKPs *)

--tqc.txt--

Computed bands:  9 - 13
GM: GM1+(1); GM2-(1); GM1+(1); GM3-(2); [5]
T : T1+ (1); T2- (1); T3- (2); T2- (1); [5]
F : F1+ (1); F2- (1); F2- (1); F1- (1); F1+ (1); [5]
L : L1+ (1); L2- (1); L2- (1); L1- (1); L2- (1); [5]

--tqc.data--

166    4    5       # space group number, number of k-points, number of energy bands (nb)
1  1  4  1  6       # k index, irrep index [nb]
2  1  4  6  4
4  1  4  4  2  1
5  1  4  4  2  4

3. Solving the aBR/eBR decomposition online

Website: http://tm.iphy.ac.cn/UnconvMat.html
Ref: J. Gao, et al. "Unconventional materials: the mismatch between electronic charge centers and atomic positions" , Sci. Bul. 66, 667 (2022) https://doi.org/10.1016/j.scib.2021.12.025

$$ Paste "PPOSCAR" and "tqc.data" onto the website.

$$ Press the button "BR" to solve the eBR and aBR decompositions.

A1g@3a (N-s) + A2u@3a (N-Pz) + Eu@3a (N-Px,Py) + A1g@3b (an empty site)