### 2015-10-27 15:59:39 Title P lattice Symmorphic crystal with inversion symmetry Complex eigenfunctions Spin-orbit eigenfunctions (->;time inversion) Spin-polarization Transformations: From k-list in lapw1 to Cartesian coord. system (BR1) 1.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 1.0000 From k-list in lapw1 to prim. reciprocal space (DB1) 1.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 1.0000 SYMMETRY OPERATIONS Pi={Ri|taui+tm} Ri taui inv(Ri) Ri(Cartesian coord) Eulers angles spin transf. 1 0 0 0.000 1 0 0 1.000 0.000 0.000 0.000 0 1 0 0.000 0 1 0 0.000 1.000 0.000 0.000 ( 1.000 0.000)( 0.000 0.000) 0 0 1 0.000 0 0 1 0.000 0.000 1.000 0.000 ( 0.000 0.000)( 1.000 0.000) 1 (E) unity op. rotation through ( 1.000, 0.000, 0.000) -1 0 0 0.000 -1 0 0 -1.000 0.000 0.000 0.000 0-1 0 0.000 0-1 0 0.000-1.000 0.000 3.142 ( 0.000 1.000)( 0.000 0.000) 0 0 1 0.000 0 0 1 0.000 0.000 1.000 0.000 ( 0.000 0.000)( 0.000-1.000) 2 (C2) 180-degree rotation rotation through ( 0.000, 0.000, 1.000) 0-1 0 0.000 0 1 0 0.000-1.000 0.000 0.000 1 0 0 0.000 -1 0 0 1.000 0.000 0.000 4.712 ( 0.707-0.707)( 0.000 0.000) 0 0 1 0.000 0 0 1 0.000 0.000 1.000 0.000 ( 0.000 0.000)( 0.707 0.707) 3 (C4) 90-degree rotation clockwise rotation through ( 0.000, 0.000, 1.000) 0 1 0 0.000 0-1 0 0.000 1.000 0.000 0.000 -1 0 0 0.000 1 0 0 -1.000 0.000 0.000 1.571 ( 0.707 0.707)( 0.000 0.000) 0 0 1 0.000 0 0 1 0.000 0.000 1.000 0.000 ( 0.000 0.000)( 0.707-0.707) 4 (C4) 90-degree rotation counterclockwise rotation through ( 0.000, 0.000, 1.000) -1 0 0 0.000 -1 0 0 -1.000 0.000 0.000 0.000 0-1 0 0.000 0-1 0 0.000-1.000 0.000 0.000 ( 1.000 0.000)( 0.000 0.000) 0 0-1 0.000 0 0-1 0.000 0.000-1.000 0.000 ( 0.000 0.000)( 1.000 0.000) 5 (I) inverse op. rotation through ( 1.000, 0.000, 0.000) 1 0 0 0.000 1 0 0 1.000 0.000 0.000 0.000 0 1 0 0.000 0 1 0 0.000 1.000 0.000 3.142 ( 0.000 1.000)( 0.000 0.000) 0 0-1 0.000 0 0-1 0.000 0.000-1.000 0.000 ( 0.000 0.000)( 0.000-1.000) 6 (IC2) 180-degree rotation times inversion rotation through ( 0.000, 0.000, 1.000) 0 1 0 0.000 0-1 0 0.000 1.000 0.000 0.000 -1 0 0 0.000 1 0 0 -1.000 0.000 0.000 4.712 ( 0.707-0.707)( 0.000 0.000) 0 0-1 0.000 0 0-1 0.000 0.000-1.000 0.000 ( 0.000 0.000)( 0.707 0.707) 7 (IC4) 90-degree rotation times inversion clockwise rotation through ( 0.000, 0.000, 1.000) 0-1 0 0.000 0 1 0 0.000-1.000 0.000 0.000 1 0 0 0.000 -1 0 0 1.000 0.000 0.000 1.571 ( 0.707 0.707)( 0.000 0.000) 0 0-1 0.000 0 0-1 0.000 0.000-1.000 0.000 ( 0.000 0.000)( 0.707-0.707) 8 (IC4) 90-degree rotation times inversion counterclockwise rotation through ( 0.000, 0.000, 1.000) -1 0 0 0.000 -1 0 0 -1.000 0.000 0.000 3.142 0 1 0 0.000 0 1 0 0.000 1.000 0.000 0.000 ( 0.000 0.000)( 1.000 0.000) 0 0-1 0.000 0 0-1 0.000 0.000-1.000 0.000 (-1.000 0.000)( 0.000 0.000) 9 (C2) 180-degree rotation rotation through ( 0.000, 1.000, 0.000) 1 0 0 0.000 1 0 0 1.000 0.000 0.000 3.142 0-1 0 0.000 0-1 0 0.000-1.000 0.000 3.142 ( 0.000 0.000)( 0.000-1.000) 0 0-1 0.000 0 0-1 0.000 0.000-1.000 0.000 ( 0.000-1.000)( 0.000 0.000) 10 (C2) 180-degree rotation rotation through ( 1.000, 0.000, 0.000) 0 1 0 0.000 0 1 0 0.000 1.000 0.000 3.142 1 0 0 0.000 1 0 0 1.000 0.000 0.000 1.571 ( 0.000 0.000)( 0.707 0.707) 0 0-1 0.000 0 0-1 0.000 0.000-1.000 0.000 (-0.707 0.707)( 0.000 0.000) 11 (C2) 180-degree rotation rotation through ( 0.707, 0.707, 0.000) 0-1 0 0.000 0-1 0 0.000-1.000 0.000 3.142 -1 0 0 0.000 -1 0 0 -1.000 0.000 0.000 4.712 ( 0.000 0.000)(-0.707 0.707) 0 0-1 0.000 0 0-1 0.000 0.000-1.000 0.000 ( 0.707 0.707)( 0.000 0.000) 12 (C2) 180-degree rotation rotation through ( 0.707,-0.707, 0.000) 1 0 0 0.000 1 0 0 1.000 0.000 0.000 3.142 0-1 0 0.000 0-1 0 0.000-1.000 0.000 0.000 ( 0.000 0.000)( 1.000 0.000) 0 0 1 0.000 0 0 1 0.000 0.000 1.000 0.000 (-1.000 0.000)( 0.000 0.000) 13 (IC2) 180-degree rotation times inversion rotation through ( 0.000, 1.000, 0.000) -1 0 0 0.000 -1 0 0 -1.000 0.000 0.000 3.142 0 1 0 0.000 0 1 0 0.000 1.000 0.000 3.142 ( 0.000 0.000)( 0.000-1.000) 0 0 1 0.000 0 0 1 0.000 0.000 1.000 0.000 ( 0.000-1.000)( 0.000 0.000) 14 (IC2) 180-degree rotation times inversion rotation through ( 1.000, 0.000, 0.000) 0-1 0 0.000 0-1 0 0.000-1.000 0.000 3.142 -1 0 0 0.000 -1 0 0 -1.000 0.000 0.000 1.571 ( 0.000 0.000)( 0.707 0.707) 0 0 1 0.000 0 0 1 0.000 0.000 1.000 0.000 (-0.707 0.707)( 0.000 0.000) 15 (IC2) 180-degree rotation times inversion rotation through ( 0.707, 0.707, 0.000) 0 1 0 0.000 0 1 0 0.000 1.000 0.000 3.142 1 0 0 0.000 1 0 0 1.000 0.000 0.000 4.712 ( 0.000 0.000)(-0.707 0.707) 0 0 1 0.000 0 0 1 0.000 0.000 1.000 0.000 ( 0.707 0.707)( 0.000 0.000) 16 (IC2) 180-degree rotation times inversion rotation through ( 0.707,-0.707, 0.000) ******************************************************************************** knum = 1 kname= GAMMA k = 0.000000 0.000000 0.000000 The point group is D4h 16 symmetry operations in 10 classes Table 40 on page 50 in Koster et al [7] Table 33.4 on page 258 in Altmann et al [8] E 2C4 C2 2C2` 2C2" I 2IC4 IC2 2IC2` 2IC2" G1+ A1g 1 1 1 1 1 1 1 1 1 1 G2+ A2g 1 1 1 -1 -1 1 1 1 -1 -1 G3+ B1g 1 -1 1 1 -1 1 -1 1 1 -1 G4+ B2g 1 -1 1 -1 1 1 -1 1 -1 1 G5+ Eg 2 0 -2 0 0 2 0 -2 0 0 G1- A1u 1 1 1 1 1 -1 -1 -1 -1 -1 G2- A2u 1 1 1 -1 -1 -1 -1 -1 1 1 G3- B1u 1 -1 1 1 -1 -1 1 -1 -1 1 G4- B2u 1 -1 1 -1 1 -1 1 -1 1 -1 G5- Eu 2 0 -2 0 0 -2 0 2 0 0 -------------------------------------------------------------------- G6+ E1/2g 2 /2 0 0 0 2 /2 0 0 0 G7+ E3/2g 2 -/2 0 0 0 2 -/2 0 0 0 G6- E1/2u 2 /2 0 0 0 -2 -/2 0 0 0 G7- E3/2u 2 -/2 0 0 0 -2 /2 0 0 0 labeling of IRs can change due to choice of symmetry axes: G3 <;->; G4 class, symmetry ops, exp(-i*k*taui), main axes E 1 (+1.00+0.00i) 2C4 3 4 (+1.00+0.00i) C2 2 (+1.00+0.00i) ( 0.000, 0.000, 1.000) 2C2` 9 10 (+1.00+0.00i) ( 1.000, 0.000, 0.000) 2C2" 11 12 (+1.00+0.00i) ( 0.707,-0.707, 0.000) I 5 (+1.00+0.00i) 2IC4 7 8 (+1.00+0.00i) IC2 6 (+1.00+0.00i) 2IC2` 13 14 (+1.00+0.00i) 2IC2" 15 16 (+1.00+0.00i) bnd ndg eigval E 2C4 C2 2C2` 2C2" I 2IC4 IC2 2IC2` 2IC2" 1 1 -5.032672 1.00+0.00i 0.71-0.71i STOP: X=( 0.70711 0.70711) Xold=( 0.70711-0.70711) 3 4 2C4 X not equal for all elements in the class 0.00+1.00i 0.00+0.00i 0.00+0.00i 1.00+0.00i 0.71-0.71i STOP: X=( 0.70711 0.70711) Xold=( 0.70711-0.70711) 7 8 2IC4 X not equal for all elements in the class 0.00+1.00i 0.00+0.00i 0.00+0.00i ?? 2 1 -5.032369 1.00+0.00i 0.71-0.71i STOP: X=( 0.70711 0.70711) Xold=( 0.70711-0.70711) 3 4 2C4 X not equal for all elements in the class 0.00+1.00i 0.00+0.00i 0.00+0.00i -1.00+0.00i -0.71+0.71i STOP: X=(-0.70711-0.70711) Xold=(-0.70711 0.70711) 7 8 2IC4 X not equal for all elements in the class 0.00-1.00i 0.00+0.00i 0.00+0.00i ?? 3 1 -5.032127 1.00+0.00i -0.71+0.71i STOP: X=(-0.70711-0.70711) Xold=(-0.70711 0.70711) 3 4 2C4 X not equal for all elements in the class 0.00+1.00i 0.00+0.00i 0.00+0.00i 1.00+0.00i -0.71+0.71i STOP: X=(-0.70711-0.70711) Xold=(-0.70711 0.70711) 7 8 2IC4 X not equal for all elements in the class 0.00+1.00i 0.00+0.00i 0.00+0.00i ?? 4 1 -5.031841 1.00+0.00i -0.71+0.71i STOP: X=(-0.70711-0.70711) Xold=(-0.70711 0.70711) 3 4 2C4 X not equal for all elements in the class 0.00+1.00i 0.00+0.00i 0.00+0.00i -1.00+0.00i 0.71-0.71i STOP: X=( 0.70711 0.70711) Xold=( 0.70711-0.70711) 7 8 2IC4 X not equal for all elements in the class 0.00-1.00i 0.00+0.00i 0.00+0.00i ?? 5 1 -4.941795 1.00+0.00i 0.71+0.71i STOP: X=( 0.70711-0.70711) Xold=( 0.70711 0.70711) 3 4 2C4 X not equal for all elements in the class 0.00-1.00i 0.00+0.00i 0.00+0.00i 1.00+0.00i 0.71+0.71i STOP: X=( 0.70711-0.70711) Xold=( 0.70711 0.70711) 7 8 2IC4 X not equal for all elements in the class 0.00-1.00i 0.00+0.00i 0.00+0.00i ?? 6 1 -4.941474 1.00+0.00i 0.71+0.71i STOP: X=( 0.70711-0.70711) Xold=( 0.70711 0.70711) 3 4 2C4 X not equal for all elements in the class 0.00-1.00i 0.00+0.00i 0.00+0.00i -1.00+0.00i -0.71-0.71i STOP: X=(-0.70711 0.70711) Xold=(-0.70711-0.70711) 7 8 2IC4 X not equal for all elements in the class 0.00+1.00i 0.00+0.00i 0.00+0.00i ?? 7 1 -4.941219 1.00+0.00i -0.71-0.71i STOP: X=(-0.70711 0.70711) Xold=(-0.70711-0.70711) 3 4 2C4 X not equal for all elements in the class 0.00-1.00i 0.00+0.00i 0.00+0.00i 1.00+0.00i -0.71-0.71i STOP: X=(-0.70711 0.70711) Xold=(-0.70711-0.70711) 7 8 2IC4 X not equal for all elements in the class 0.00-1.00i 0.00+0.00i 0.00+0.00i ?? 8 1 -4.940916 1.00+0.00i -0.71-0.71i STOP: X=(-0.70711 0.70711) Xold=(-0.70711-0.70711) 3 4 2C4 X not equal for all elements in the class 0.00-1.00i 0.00+0.00i 0.00+0.00i -1.00+0.00i 0.71+0.71i STOP: X=( 0.70711-0.70711) Xold=( 0.70711 0.70711) 7 8 2IC4 X not equal for all elements in the class 0.00+1.00i 0.00+0.00i 0.00+0.00i ?? 9 1 -2.784170 1.00+0.00i -0.71-0.71i STOP: X=(-0.70711 0.70711) Xold=(-0.70711-0.70711) 3 4 2C4 X not equal for all elements in the class 0.00-1.00i 0.00+0.00i 0.00+0.00i -1.00+0.00i 0.71+0.71i STOP: X=( 0.70711-0.70711) Xold=( 0.70711 0.70711) 7 8 2IC4 X not equal for all elements in the class 0.00+1.00i 0.00+0.00i 0.00+0.00i ?? 10 1 -2.784049 1.00+0.00i -0.71-0.71i STOP: X=(-0.70711 0.70711) Xold=(-0.70711-0.70711) 3 4 2C4 X not equal for all elements in the class 0.00-1.00i 0.00+0.00i 0.00+0.00i 1.00+0.00i -0.71-0.71i STOP: X=(-0.70711 0.70711) Xold=(-0.70711-0.70711) 7 8 2IC4 X not equal for all elements in the class 0.00-1.00i 0.00+0.00i 0.00+0.00i ?? 11 1 -2.781872 1.00+0.00i 0.71+0.71i STOP: X=( 0.70711-0.70711) Xold=( 0.70711 0.70711) 3 4 2C4 X not equal for all elements in the class 0.00-1.00i 0.00+0.00i 0.00+0.00i 1.00+0.00i 0.71+0.71i STOP: X=( 0.70711-0.70711) Xold=( 0.70711 0.70711) 7 8 2IC4 X not equal for all elements in the class 0.00-1.00i 0.00+0.00i 0.00+0.00i ?? 12 1 -2.781326 1.00+0.00i 0.71+0.71i STOP: X=( 0.70711-0.70711) Xold=( 0.70711 0.70711) 3 4 2C4 X not equal for all elements in the class 0.00-1.00i 0.00+0.00i 0.00+0.00i -1.00+0.00i -0.71-0.71i STOP: X=(-0.70711 0.70711) Xold=(-0.70711-0.70711) 7 8 2IC4 X not equal for all elements in the class 0.00+1.00i 0.00+0.00i 0.00+0.00i ?? 13 1 -2.766987 1.00+0.00i 0.71-0.71i STOP: X=( 0.70711 0.70711) Xold=( 0.70711-0.70711) 3 4 2C4 X not equal for all elements in the class 0.00+1.00i 0.00+0.00i 0.00+0.00i 1.00+0.00i 0.71-0.71i STOP: X=( 0.70711 0.70711) Xold=( 0.70711-0.70711) 7 8 2IC4 X not equal for all elements in the class 0.00+1.00i 0.00+0.00i 0.00+0.00i ?? 14 1 -2.761775 1.00+0.00i -0.71+0.71i STOP: X=(-0.70711-0.70711) Xold=(-0.70711 0.70711) 3 4 2C4 X not equal for all elements in the class 0.00+1.00i 0.00+0.00i 0.00+0.00i 1.00+0.00i -0.71+0.71i STOP: X=(-0.70711-0.70711) Xold=(-0.70711 0.70711) 7 8 2IC4 X not equal for all elements in the class 0.00+1.00i 0.00+0.00i 0.00+0.00i ?? 15 1 -2.759002 1.00+0.00i -0.71+0.71i STOP: X=(-0.70711-0.70711) Xold=(-0.70711 0.70711) 3 4 2C4 X not equal for all elements in the class 0.00+1.00i 0.00+0.00i 0.00+0.00i -1.00+0.00i 0.71-0.71i STOP: X=( 0.70711 0.70711) Xold=( 0.70711-0.70711) 7 8 2IC4 X not equal for all elements in the class 0.00-1.00i 0.00+0.00i 0.00+0.00i ?? 16 1 -2.758800 1.00+0.00i 0.71-0.71i STOP: X=( 0.70711 0.70711) Xold=( 0.70711-0.70711) 3 4 2C4 X not equal for all elements in the class 0.00+1.00i 0.00+0.00i 0.00+0.00i -1.00+0.00i -0.71+0.71i STOP: X=(-0.70711-0.70711) Xold=(-0.70711 0.70711) 7 8 2IC4 X not equal for all elements in the class 0.00-1.00i 0.00+0.00i 0.00+0.00i ?? 17 1 -2.736477 1.00+0.00i 0.71+0.71i STOP: X=( 0.70711-0.70711) Xold=( 0.70711 0.70711) 3 4 2C4 X not equal for all elements in the class 0.00-1.00i 0.00+0.00i 0.00+0.00i 1.00+0.00i 0.71+0.71i STOP: X=( 0.70711-0.70711) Xold=( 0.70711 0.70711) 7 8 2IC4 X not equal for all elements in the class 0.00-1.00i 0.00+0.00i 0.00+0.00i ?? 18 1 -2.734773 1.00+0.00i 0.71+0.71i STOP: X=( 0.70711-0.70711) Xold=( 0.70711 0.70711) 3 4 2C4 X not equal for all elements in the class 0.00-1.00i 0.00+0.00i 0.00+0.00i 1.00+0.00i 0.71+0.71i STOP: X=( 0.70711-0.70711) Xold=( 0.70711 0.70711) 7 8 2IC4 X not equal for all elements in the class 0.00-1.00i 0.00+0.00i 0.00+0.00i ?? 19 1 -2.724771 1.00+0.00i 0.71-0.71i STOP: X=( 0.70711 0.70711) Xold=( 0.70711-0.70711) 3 4 2C4 X not equal for all elements in the class 0.00+1.00i 0.00+0.00i 0.00+0.00i 1.00+0.00i 0.71-0.71i STOP: X=( 0.70711 0.70711) Xold=( 0.70711-0.70711) 7 8 2IC4 X not equal for all elements in the class 0.00+1.00i 0.00+0.00i 0.00+0.00i ?? 20 1 -2.719841 1.00+0.00i 0.71-0.71i STOP: X=( 0.70711 0.70711) Xold=( 0.70711-0.70711) 3 4 2C4 X not equal for all elements in the class 0.00+1.00i 0.00+0.00i 0.00+0.00i 1.00+0.00i 0.71-0.71i STOP: X=( 0.70711 0.70711) Xold=( 0.70711-0.70711) 7 8 2IC4 X not equal for all elements in the class 0.00+1.00i 0.00+0.00i 0.00+0.00i ?? 21 1 -2.709608 1.00+0.00i 0.71+0.71i STOP: X=( 0.70711-0.70711) Xold=( 0.70711 0.70711) 3 4 2C4 X not equal for all elements in the class 0.00-1.00i 0.00+0.00i 0.00+0.00i -1.00+0.00i -0.71-0.71i STOP: X=(-0.70711 0.70711) Xold=(-0.70711-0.70711) 7 8 2IC4 X not equal for all elements in the class 0.00+1.00i 0.00+0.00i 0.00+0.00i ?? 22 1 -2.709053 1.00+0.00i 0.71+0.71i STOP: X=( 0.70711-0.70711) Xold=( 0.70711 0.70711) 3 4 2C4 X not equal for all elements in the class 0.00-1.00i 0.00+0.00i 0.00+0.00i 1.00+0.00i 0.71+0.71i STOP: X=( 0.70711-0.70711) Xold=( 0.70711 0.70711) 7 8 2IC4 X not equal for all elements in the class 0.00-1.00i 0.00+0.00i 0.00+0.00i ?? 23 1 -2.706103 1.00+0.00i -0.71-0.71i STOP: X=(-0.70711 0.70711) Xold=(-0.70711-0.70711) 3 4 2C4 X not equal for all elements in the class 0.00-1.00i 0.00+0.00i 0.00+0.00i -1.00+0.00i 0.71+0.71i STOP: X=( 0.70711-0.70711) Xold=( 0.70711 0.70711) 7 8 2IC4 X not equal for all elements in the class 0.00+1.00i 0.00+0.00i 0.00+0.00i ?? 24 1 -2.705670 1.00+0.00i -0.71-0.71i STOP: X=(-0.70711 0.70711) Xold=(-0.70711-0.70711) 3 4 2C4 X not equal for all elements in the class 0.00-1.00i 0.00+0.00i 0.00+0.00i 1.00+0.00i -0.71-0.71i STOP: X=(-0.70711 0.70711) Xold=(-0.70711-0.70711) 7 8 2IC4 ******************************************************************************** TOTAL TIME: 0.17 ERROR: irrep inconsistency:no of egval 1