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quantum-espresso/PW/divide_class_so.f90

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Now bands.x can classify the bands according to the irreducible representation of the small group of k. k points on the border of the Brillouin zone of systems with non symmorphic space groups are not dealt with. Spin-orbit case included. Find_mode_sym extended to all the q points, with the same limitations as the bands. (still experimental). git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3330 c92efa57-630b-4861-b058-cf58834340f0
2006-08-23 01:01:13 +08:00
!
! Copyright (C) 2006 Quantum-ESPRESSO group
! This file is distributed under the terms of the
! GNU General Public License. See the file `License'
! in the root directory of the present distribution,
! or http://www.gnu.org/copyleft/gpl.txt .
!
#include "f_defs.h"
!
!-----------------------------------------------------------------------------
SUBROUTINE divide_class_so(code_group,nrot,smat,d_spin,has_e,nclass, &
nelem,elem, which_irr)
!-----------------------------------------------------------------------------
!
! This subroutine receives as input a set of nrot 3x3 matrices smat,
! and nrot complex 2x2 matrices d_spin, which are assumed to be the
! operations of the point group given by code_group. Only the operations
! that do not contain the 2\pi rotation (-E) are given in input.
! smat are in cartesian coordinates.
! This routine divides the double group in classes and find:
!
! nclass the number of classes of the double group
! nelem(iclass) for each class, the number of elements of the class
! elem(i,iclass) 1<i<nelem(iclass) for each class tells which matrices
! smat belong to that class
! has_e(i,iclass) =-1 if the operation is multiplied by -E, 1 otherwise
! which_irr(iclass) for each class gives the position of that class in the
! character table associated with the group and provided
! by the routine set_irr_rap_so. NB: changing the order of
! the elements in the character table must reflect in
! a change to which_irr. Presently the character tables
! are those given by G.F. Koster, Space Group and their
! representations.
! Several equivalent names for the irreducible representation
! are given. D, G, L, S are used for Delta, Gamma, Lambda
! and Sigma.
!
USE kinds, ONLY : DP
IMPLICIT NONE
INTEGER :: &
code_group, & ! The code of the point group
nrot, & ! The number of symmetry operation
nclass, & ! The number of classes
nelem(24), & ! The elements of each class
elem(12,24), & ! Which elements in the smat list for each class
has_e(12,24), & ! if -1 the element is multiplied by -E
which_irr(24) ! See above
REAL(DP) :: smat(3,3,nrot), cmat(3,3), ax(3)
REAL(DP) :: smate(3,3,2*nrot)
COMPLEX(DP) :: d_spin(2,2,48), d_spine(2,2,96), c_spin(2,2)
More patches from Axel: - correct an unquoted string (iosys) in PW/input.f90:483 (this was the cause of tonight compilation failere) - correct a few incorrect format strings - make more use of the constants module and thus provide more consistent units. NOTE, this has some numerical changes in the outputs, as in some places rather low precision and inconsistent numbers were used for unit conversion. - convert all(?) single precision constants to double using the attached little perl program. exceptions: efermi.f90 (as it is supposed to be rewritten anyways), plotbands.f90 (it uses single precision everywhere, which may result in saving a significant amount of memory, so i converted the two double precision constants to single). Unused routine 'set_fft_grid' removed git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3602 c92efa57-630b-4861-b058-cf58834340f0
2006-12-14 16:53:47 +08:00
INTEGER :: done(96), irot, jrot, krot, iclass, i
Now bands.x can classify the bands according to the irreducible representation of the small group of k. k points on the border of the Brillouin zone of systems with non symmorphic space groups are not dealt with. Spin-orbit case included. Find_mode_sym extended to all the q points, with the same limitations as the bands. (still experimental). git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3330 c92efa57-630b-4861-b058-cf58834340f0
2006-08-23 01:01:13 +08:00
INTEGER :: tipo_sym, set_e, ipol, axis, axis1, axis2, ts
REAL(DP), PARAMETER :: eps = 1.d-7
REAL(DP) :: angle_rot, angle_rot_s, ars
LOGICAL :: compare_mat_so, is_axis, first, first1
Symmetry analysis was not working for a D_2h point group with rotation axis not coincident with the coordinate axis. git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3471 c92efa57-630b-4861-b058-cf58834340f0
2006-10-21 23:09:19 +08:00
LOGICAL :: done_ax(6)
Now bands.x can classify the bands according to the irreducible representation of the small group of k. k points on the border of the Brillouin zone of systems with non symmorphic space groups are not dealt with. Spin-orbit case included. Find_mode_sym extended to all the q points, with the same limitations as the bands. (still experimental). git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3330 c92efa57-630b-4861-b058-cf58834340f0
2006-08-23 01:01:13 +08:00
!
! Divide the group in classes.
!
DO irot=1,nrot
smate(:,:,irot)=smat(:,:,irot)
smate(:,:,irot+nrot)=smat(:,:,irot)
d_spine(:,:,irot)=d_spin(:,:,irot)
d_spine(:,:,irot+nrot)=-d_spin(:,:,irot)
END DO
!
! If there are doubts that the input matrices are not a point group uncomment
! the call to this routine.
!
!CALL check_tgroup(2*nrot,d_spine,smate)
!
nclass=0
nelem=0
done=0
DO irot=1,2*nrot
IF (done(irot)==0) THEN
nclass=nclass+1
DO jrot=1,2*nrot
CALL coniug_mat_so(smate(1,1,jrot),d_spine(1,1,jrot), &
smate(1,1,irot),d_spine(1,1,irot), &
cmat,c_spin)
DO krot=1,2*nrot
IF (compare_mat_so(cmat,c_spin,smate(1,1,krot),d_spine(1,1,krot)) &
.AND.done(krot)==0) THEN
nelem(nclass)=nelem(nclass)+1
IF (krot.le.nrot) THEN
elem(nelem(nclass),nclass)=krot
has_e(nelem(nclass),nclass)=1
ELSE
elem(nelem(nclass),nclass)=krot-nrot
has_e(nelem(nclass),nclass)=-1
ENDIF
done(krot)=1
ENDIF
ENDDO
ENDDO
ENDIF
ENDDO
!
! For each class we should now decide which_irr. This depends on the group
! and on the tables of characters of the irreducible representation.
!
which_irr(1)=1
IF (code_group==1) THEN
!
! C_1
!
which_irr(2)=2
ELSEIF (code_group==2.OR.code_group==3.OR.code_group==4) THEN
!
! C_i, C_s, C_2
!
DO iclass=2,nclass
IF (tipo_sym(smat(1,1,elem(1,iclass)))==1) THEN
which_irr(iclass)=2
ELSE
which_irr(iclass)=set_e(has_e(1,iclass),3)
END IF
END DO
ELSEIF (code_group==5) THEN
!
! C_3
!
! The function angle_rot(smat) provides the rotation angle of the matrix smat
!
DO iclass=2,nclass
IF (tipo_sym(smat(1,1,elem(1,iclass)))==1) THEN
which_irr(iclass)=2
ELSE
IF (ABS(angle_rot(smat(1,1,elem(1,iclass)))-120.d0)<eps) THEN
which_irr(iclass)=set_e(has_e(1,iclass),3)
ELSE
which_irr(iclass)=set_e(has_e(1,iclass),5)
ENDIF
ENDIF
ENDDO
ELSEIF (code_group==6) THEN
!
! C_4
!
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==1) THEN
which_irr(iclass)=2
ELSEIF (ts==4) THEN
which_irr(iclass)=set_e(has_e(1,iclass),5)
ELSEIF (ts==3) THEN
ars=angle_rot(smat(1,1,elem(1,iclass)))
IF (ABS(ars-90.d0)<eps) THEN
which_irr(iclass)=set_e(has_e(1,iclass),3)
ELSEIF (ABS(ars-270.d0)<eps) THEN
which_irr(iclass)=set_e(has_e(1,iclass),7)
ELSE
CALL errore('divide_class_so','wrong angle',1)
ENDIF
ELSE
CALL errore('divide_class_so','wrong sym_type',1)
ENDIF
ENDDO
ELSEIF (code_group==7) THEN
!
! C_6
!
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==1) THEN
which_irr(iclass)=2
ELSE IF (ts==4) THEN
which_irr(iclass)=set_e(has_e(1,iclass),7)
ELSEIF (ts==3) THEN
ars=angle_rot(smat(1,1,elem(1,iclass)))
IF (ABS(ars-60.d0)<eps) THEN
which_irr(iclass)=set_e(has_e(1,iclass),3)
ELSEIF (ABS(ars-120.d0)<eps) THEN
which_irr(iclass)=set_e(has_e(1,iclass),5)
ELSEIF (ABS(ars-240.d0)<eps) THEN
which_irr(iclass)=set_e(has_e(1,iclass),9)
ELSEIF (ABS(ars-300.d0)<eps) THEN
which_irr(iclass)=set_e(has_e(1,iclass),11)
ELSE
CALL errore('divide_class_so','wrong angle',1)
ENDIF
ELSE
CALL errore('divide_class_so','wrong sym_type',1)
ENDIF
ENDDO
ELSEIF (code_group==8) THEN
!
! D_2
!
Fixed a problem with D_2 classes. Problem found by Tao Sun. git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@4142 c92efa57-630b-4861-b058-cf58834340f0
2007-08-16 17:33:49 +08:00
first=.true.
Now bands.x can classify the bands according to the irreducible representation of the small group of k. k points on the border of the Brillouin zone of systems with non symmorphic space groups are not dealt with. Spin-orbit case included. Find_mode_sym extended to all the q points, with the same limitations as the bands. (still experimental). git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3330 c92efa57-630b-4861-b058-cf58834340f0
2006-08-23 01:01:13 +08:00
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==1) THEN
which_irr(iclass)=2
Fixed a problem with D_2 classes. Problem found by Tao Sun. git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@4142 c92efa57-630b-4861-b058-cf58834340f0
2007-08-16 17:33:49 +08:00
first=.false.
Now bands.x can classify the bands according to the irreducible representation of the small group of k. k points on the border of the Brillouin zone of systems with non symmorphic space groups are not dealt with. Spin-orbit case included. Find_mode_sym extended to all the q points, with the same limitations as the bands. (still experimental). git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3330 c92efa57-630b-4861-b058-cf58834340f0
2006-08-23 01:01:13 +08:00
ELSE
Fixed a problem with D_2 classes. Problem found by Tao Sun. git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@4142 c92efa57-630b-4861-b058-cf58834340f0
2007-08-16 17:33:49 +08:00
if (first) then
which_irr(iclass)=iclass+1
else
which_irr(iclass)=iclass
endif
Now bands.x can classify the bands according to the irreducible representation of the small group of k. k points on the border of the Brillouin zone of systems with non symmorphic space groups are not dealt with. Spin-orbit case included. Find_mode_sym extended to all the q points, with the same limitations as the bands. (still experimental). git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3330 c92efa57-630b-4861-b058-cf58834340f0
2006-08-23 01:01:13 +08:00
END IF
ENDDO
ELSEIF (code_group==9) THEN
!
! D_3
!
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==1) THEN
which_irr(iclass)=2
ELSE IF (ts==4) THEN
which_irr(iclass)=set_e(has_e(1,iclass),5)
ELSEIF (ts==3) THEN
which_irr(iclass)=set_e(has_e(1,iclass),3)
ELSE
CALL errore('divide_class_so','wrong sym_type',1)
ENDIF
ENDDO
ELSEIF (code_group==10) THEN
!
! D_4
!
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==3) THEN
which_irr(iclass)=set_e(has_e(1,iclass),3)
CALL versor(smat(1,1,elem(1,iclass)),ax)
axis=0
DO ipol=1,3
IF (is_axis(ax,ipol)) axis=ipol
ENDDO
axis1=MOD(ipol,3)+1
axis2=MOD(ipol+1,3)+1
Bug fix: problems with D_4 group. (Contributed by M. Lazzeri) git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@4505 c92efa57-630b-4861-b058-cf58834340f0
2007-12-06 00:39:20 +08:00
IF (axis==0) call errore('divide_class_so','unknown D_4 axis ',1)
Now bands.x can classify the bands according to the irreducible representation of the small group of k. k points on the border of the Brillouin zone of systems with non symmorphic space groups are not dealt with. Spin-orbit case included. Find_mode_sym extended to all the q points, with the same limitations as the bands. (still experimental). git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3330 c92efa57-630b-4861-b058-cf58834340f0
2006-08-23 01:01:13 +08:00
ENDIF
END DO
first=.TRUE.
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==1) THEN
which_irr(iclass)=2
ELSEIF (ts==4) THEN
CALL versor(smat(1,1,elem(1,iclass)),ax)
IF (is_axis(ax,axis)) THEN
which_irr(iclass)=5
ELSEIF (is_axis(ax,axis1).or.is_axis(ax,axis2)) THEN
which_irr(iclass)=6
ELSE
which_irr(iclass)=7
END IF
Bug fix: problems with D_4 group. (Contributed by M. Lazzeri) git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@4505 c92efa57-630b-4861-b058-cf58834340f0
2007-12-06 00:39:20 +08:00
ELSEIF (ts.ne.3) THEN
Now bands.x can classify the bands according to the irreducible representation of the small group of k. k points on the border of the Brillouin zone of systems with non symmorphic space groups are not dealt with. Spin-orbit case included. Find_mode_sym extended to all the q points, with the same limitations as the bands. (still experimental). git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3330 c92efa57-630b-4861-b058-cf58834340f0
2006-08-23 01:01:13 +08:00
CALL errore('divide_class_so','wrong sym_type',1)
END IF
END DO
ELSEIF (code_group==11) THEN
!
! D_6
!
first=.true.
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==1) THEN
which_irr(iclass)=2
ELSE IF (ts==3) THEN
ars=angle_rot(smat(1,1,elem(1,iclass)))
IF ((ABS(ars-60.d0)<eps).OR.(ABS(ars-300.d0)<eps) ) THEN
which_irr(iclass)=set_e(has_e(1,iclass),6)
ELSE
which_irr(iclass)=set_e(has_e(1,iclass),4)
ENDIF
ELSEIF (ts==4) THEN
CALL versor(smat(1,1,elem(1,iclass)),ax)
IF (is_axis(ax,3)) THEN
which_irr(iclass)=3
ELSE
IF (first) THEN
which_irr(iclass)=8
first=.false.
ELSE
which_irr(iclass)=9
END IF
END IF
ELSE
CALL errore('divide_class_so','wrong sym_type',1)
END IF
END DO
ELSEIF (code_group==12) THEN
!
! C_2v
!
first=.true.
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==1) THEN
which_irr(iclass)=2
ELSEIF (ts==4) THEN
which_irr(iclass)=3
ELSEIF (ts==5.and.first) THEN
which_irr(iclass)=4
first=.false.
ELSE
which_irr(iclass)=5
ENDIF
ENDDO
ELSEIF (code_group==13) THEN
!
! C_3v
!
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==1) THEN
which_irr(iclass)=2
ELSEIF (ts==3) THEN
which_irr(iclass)=set_e(has_e(1,iclass),3)
ELSEIF (ts==5) THEN
which_irr(iclass)=set_e(has_e(1,iclass),5)
ELSE
CALL errore('divide_class_so','wrong operation',1)
ENDIF
ENDDO
ELSEIF (code_group==14) THEN
!
! C_4v
!
first=.true.
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==1) THEN
which_irr(iclass)=2
ELSEIF (ts==3) THEN
which_irr(iclass)=set_e(has_e(1,iclass),3)
ELSEIF (ts==4) THEN
which_irr(iclass)=5
ELSEIF (ts==5.and.first) THEN
which_irr(iclass)=6
first=.false.
ELSE
which_irr(iclass)=7
ENDIF
ENDDO
ELSEIF (code_group==15) THEN
!
! C_6v
!
first=.true.
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==1) THEN
which_irr(iclass)=2
ELSE IF (ts==3) THEN
ars=angle_rot(smat(1,1,elem(1,iclass)))
IF ((ABS(ars-60.d0)<eps).OR.(ABS(ars-300.d0)<eps)) THEN
which_irr(iclass)=set_e(has_e(1,iclass),6)
ELSE
which_irr(iclass)=set_e(has_e(1,iclass),4)
ENDIF
ELSEIF (ts==4) THEN
which_irr(iclass)=3
ELSEIF (ts==5.and.first) THEN
which_irr(iclass)=8
first=.false.
ELSE
which_irr(iclass)=9
ENDIF
ENDDO
ELSEIF (code_group==16) THEN
!
! C_2h
!
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==1) THEN
which_irr(iclass)=2
ELSEIF (ts==4) THEN
which_irr(iclass)=set_e(has_e(1,iclass),3)
ELSEIF (ts==2) THEN
which_irr(iclass)=set_e(has_e(1,iclass),7)
ELSEIF (ts==5) THEN
which_irr(iclass)=set_e(has_e(1,iclass),5)
ELSE
CALL errore('divide_class_so','wrong sym_type',1)
ENDIF
ENDDO
ELSEIF (code_group==17) THEN
!
! C_3h
!
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==1) THEN
which_irr(iclass)=2
ELSE IF (ts==3) THEN
ars=angle_rot(smat(1,1,elem(1,iclass)))
IF (ABS(ars-120.d0)<eps) THEN
which_irr(iclass)=set_e(has_e(1,iclass),3)
ELSE
which_irr(iclass)=set_e(has_e(1,iclass),5)
END IF
ELSEIF (ts==5) THEN
which_irr(iclass)=set_e(has_e(1,iclass),7)
ELSEIF (ts==6) THEN
IF (ABS(angle_rot_s(smat(1,1,elem(1,iclass)))-120.d0)<eps) THEN
which_irr(iclass)=set_e(has_e(1,iclass),9)
ELSE
which_irr(iclass)=set_e(has_e(1,iclass),11)
END IF
ELSE
CALL errore('divide_class_so','wrong sym_type',1)
ENDIF
ENDDO
ELSEIF (code_group==18) THEN
!
! C_4h
!
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==1) THEN
which_irr(iclass)=2
ELSE IF (ts==3) THEN
IF (angle_rot(smat(1,1,elem(1,iclass)))-90.d0<eps) THEN
which_irr(iclass)=set_e(has_e(1,iclass),3)
ELSE
which_irr(iclass)=set_e(has_e(1,iclass),7)
END IF
ELSEIF (ts==4) THEN
which_irr(iclass)=set_e(has_e(1,iclass),5)
ELSEIF (ts==2) THEN
which_irr(iclass)=set_e(has_e(1,iclass),9)
ELSEIF (ts==5) THEN
which_irr(iclass)=set_e(has_e(1,iclass),13)
ELSEIF (ts==6) THEN
IF (angle_rot_s(smat(1,1,elem(1,iclass)))-90.d0<eps) THEN
which_irr(iclass)=set_e(has_e(1,iclass),11)
ELSE
which_irr(iclass)=set_e(has_e(1,iclass),15)
END IF
ELSE
CALL errore('divide_class_so','wrong operation',1)
END IF
END DO
ELSEIF (code_group==19) THEN
!
! C_6h
!
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==1) THEN
which_irr(iclass)=2
ELSE IF (ts==3) THEN
ars=angle_rot(smat(1,1,elem(1,iclass)))
IF (ABS(ars-60.d0)<eps) THEN
which_irr(iclass)=set_e(has_e(1,iclass),3)
ELSEIF (ABS(ars-120.d0)<eps) THEN
which_irr(iclass)=set_e(has_e(1,iclass),5)
ELSEIF (ABS(ars-240.d0)<eps) THEN
which_irr(iclass)=set_e(has_e(1,iclass),9)
ELSEIF (ABS(ars-300.d0)<eps) THEN
which_irr(iclass)=set_e(has_e(1,iclass),11)
END IF
ELSEIF (ts==4) THEN
which_irr(iclass)=set_e(has_e(1,iclass),7)
ELSEIF (ts==2) THEN
which_irr(iclass)=set_e(has_e(1,iclass),13)
ELSEIF (ts==5) THEN
which_irr(iclass)=set_e(has_e(1,iclass),19)
ELSEIF (ts==6) THEN
ars=angle_rot_s(smat(1,1,elem(1,iclass)))
IF (ABS(ars-60.d0)<eps) THEN
Bug fix. Bug reported in S_6 by Marino Vetuschi Zuccolini. Possible problems also in: S_4, S_6, T_h, C_3h, C_4h, C_6h. git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@5185 c92efa57-630b-4861-b058-cf58834340f0
2008-09-09 23:25:55 +08:00
which_irr(iclass)=set_e(has_e(1,iclass),21)
Now bands.x can classify the bands according to the irreducible representation of the small group of k. k points on the border of the Brillouin zone of systems with non symmorphic space groups are not dealt with. Spin-orbit case included. Find_mode_sym extended to all the q points, with the same limitations as the bands. (still experimental). git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3330 c92efa57-630b-4861-b058-cf58834340f0
2006-08-23 01:01:13 +08:00
ELSEIF (ABS(ars-120.d0)<eps) THEN
Bug fix. Bug reported in S_6 by Marino Vetuschi Zuccolini. Possible problems also in: S_4, S_6, T_h, C_3h, C_4h, C_6h. git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@5185 c92efa57-630b-4861-b058-cf58834340f0
2008-09-09 23:25:55 +08:00
which_irr(iclass)=set_e(has_e(1,iclass),23)
Now bands.x can classify the bands according to the irreducible representation of the small group of k. k points on the border of the Brillouin zone of systems with non symmorphic space groups are not dealt with. Spin-orbit case included. Find_mode_sym extended to all the q points, with the same limitations as the bands. (still experimental). git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3330 c92efa57-630b-4861-b058-cf58834340f0
2006-08-23 01:01:13 +08:00
ELSEIF (ABS(ars-240.d0)<eps) THEN
Bug fix. Bug reported in S_6 by Marino Vetuschi Zuccolini. Possible problems also in: S_4, S_6, T_h, C_3h, C_4h, C_6h. git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@5185 c92efa57-630b-4861-b058-cf58834340f0
2008-09-09 23:25:55 +08:00
which_irr(iclass)=set_e(has_e(1,iclass),15)
Now bands.x can classify the bands according to the irreducible representation of the small group of k. k points on the border of the Brillouin zone of systems with non symmorphic space groups are not dealt with. Spin-orbit case included. Find_mode_sym extended to all the q points, with the same limitations as the bands. (still experimental). git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3330 c92efa57-630b-4861-b058-cf58834340f0
2006-08-23 01:01:13 +08:00
ELSEIF (ABS(ars-300.d0)<eps) THEN
Bug fix. Bug reported in S_6 by Marino Vetuschi Zuccolini. Possible problems also in: S_4, S_6, T_h, C_3h, C_4h, C_6h. git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@5185 c92efa57-630b-4861-b058-cf58834340f0
2008-09-09 23:25:55 +08:00
which_irr(iclass)=set_e(has_e(1,iclass),17)
Now bands.x can classify the bands according to the irreducible representation of the small group of k. k points on the border of the Brillouin zone of systems with non symmorphic space groups are not dealt with. Spin-orbit case included. Find_mode_sym extended to all the q points, with the same limitations as the bands. (still experimental). git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3330 c92efa57-630b-4861-b058-cf58834340f0
2006-08-23 01:01:13 +08:00
END IF
ELSE
CALL errore('divide_class_so','wrong operation',1)
ENDIF
ENDDO
ELSEIF (code_group==20) THEN
!
! D_2h
!
! mirror_axis gives the normal to the mirror plane
!
Symmetry analysis was not working for a D_2h point group with rotation axis not coincident with the coordinate axis. git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3471 c92efa57-630b-4861-b058-cf58834340f0
2006-10-21 23:09:19 +08:00
done_ax=.TRUE.
Now bands.x can classify the bands according to the irreducible representation of the small group of k. k points on the border of the Brillouin zone of systems with non symmorphic space groups are not dealt with. Spin-orbit case included. Find_mode_sym extended to all the q points, with the same limitations as the bands. (still experimental). git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3330 c92efa57-630b-4861-b058-cf58834340f0
2006-08-23 01:01:13 +08:00
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==1) THEN
which_irr(iclass)=2
ELSE IF (ts==4) THEN
CALL versor(smat(1,1,elem(1,iclass)),ax)
IF (is_axis(ax,3)) THEN
which_irr(iclass)=3
Symmetry analysis was not working for a D_2h point group with rotation axis not coincident with the coordinate axis. git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3471 c92efa57-630b-4861-b058-cf58834340f0
2006-10-21 23:09:19 +08:00
done_ax(1)=.FALSE.
Now bands.x can classify the bands according to the irreducible representation of the small group of k. k points on the border of the Brillouin zone of systems with non symmorphic space groups are not dealt with. Spin-orbit case included. Find_mode_sym extended to all the q points, with the same limitations as the bands. (still experimental). git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3330 c92efa57-630b-4861-b058-cf58834340f0
2006-08-23 01:01:13 +08:00
ELSE IF (is_axis(ax,2)) THEN
which_irr(iclass)=4
Symmetry analysis was not working for a D_2h point group with rotation axis not coincident with the coordinate axis. git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3471 c92efa57-630b-4861-b058-cf58834340f0
2006-10-21 23:09:19 +08:00
done_ax(2)=.FALSE.
Now bands.x can classify the bands according to the irreducible representation of the small group of k. k points on the border of the Brillouin zone of systems with non symmorphic space groups are not dealt with. Spin-orbit case included. Find_mode_sym extended to all the q points, with the same limitations as the bands. (still experimental). git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3330 c92efa57-630b-4861-b058-cf58834340f0
2006-08-23 01:01:13 +08:00
ELSE IF (is_axis(ax,1)) THEN
which_irr(iclass)=5
Symmetry analysis was not working for a D_2h point group with rotation axis not coincident with the coordinate axis. git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3471 c92efa57-630b-4861-b058-cf58834340f0
2006-10-21 23:09:19 +08:00
done_ax(3)=.FALSE.
ELSE
DO i=1,3
IF (done_ax(i)) THEN
which_irr(iclass)=i+2
done_ax(i)=.FALSE.
GOTO 100
END IF
END DO
100 CONTINUE
Now bands.x can classify the bands according to the irreducible representation of the small group of k. k points on the border of the Brillouin zone of systems with non symmorphic space groups are not dealt with. Spin-orbit case included. Find_mode_sym extended to all the q points, with the same limitations as the bands. (still experimental). git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3330 c92efa57-630b-4861-b058-cf58834340f0
2006-08-23 01:01:13 +08:00
END IF
ELSEIF (ts==2) THEN
IF (has_e(1,iclass)==-1) THEN
which_irr(iclass)=7
ELSE
which_irr(iclass)=6
END IF
ELSEIF (ts==5) THEN
CALL mirror_axis(smat(1,1,elem(1,iclass)),ax)
IF (is_axis(ax,3)) THEN
which_irr(iclass)=8
ELSE IF (is_axis(ax,2)) THEN
which_irr(iclass)=9
ELSE IF (is_axis(ax,1)) THEN
which_irr(iclass)=10
Symmetry analysis was not working for a D_2h point group with rotation axis not coincident with the coordinate axis. git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3471 c92efa57-630b-4861-b058-cf58834340f0
2006-10-21 23:09:19 +08:00
ELSE
DO i=4,6
IF (done_ax(i)) THEN
which_irr(iclass)=i+4
done_ax(i)=.FALSE.
GOTO 110
END IF
END DO
110 CONTINUE
Now bands.x can classify the bands according to the irreducible representation of the small group of k. k points on the border of the Brillouin zone of systems with non symmorphic space groups are not dealt with. Spin-orbit case included. Find_mode_sym extended to all the q points, with the same limitations as the bands. (still experimental). git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3330 c92efa57-630b-4861-b058-cf58834340f0
2006-08-23 01:01:13 +08:00
END IF
END IF
END DO
ELSEIF (code_group==21) THEN
!
! D_3h
!
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==1) THEN
which_irr(iclass)=2
ELSE IF (ts==3) THEN
which_irr(iclass)=set_e(has_e(1,iclass),3)
ELSE IF (ts==4) THEN
which_irr(iclass)=5
ELSE IF (ts==5) THEN
IF (nelem(iclass)>1) THEN
which_irr(iclass)=9
ELSE
which_irr(iclass)=6
END IF
ELSE IF (ts==6) THEN
which_irr(iclass)=set_e(has_e(1,iclass),7)
END IF
END DO
ELSEIF (code_group==22) THEN
!
! D_4h
!
! First search the order 4 axis
!
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==3) THEN
which_irr(iclass)=set_e(has_e(1,iclass),3)
CALL versor(smat(1,1,elem(1,iclass)),ax)
axis=0
DO ipol=1,3
IF (is_axis(ax,ipol)) axis=ipol
ENDDO
IF (axis==0) call errore('divide_class_so','unknown D_4h axis ',1)
ENDIF
END DO
first=.TRUE.
first1=.TRUE.
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==1) THEN
which_irr(iclass)=2
ELSE IF (ts==4) THEN
CALL versor(smat(1,1,elem(1,iclass)),ax)
IF (is_axis(ax,axis)) THEN
which_irr(iclass)=5
ELSE
IF (first) THEN
which_irr(iclass)=6
first=.FALSE.
ELSE
which_irr(iclass)=7
END IF
END IF
ELSEIF (ts==2) THEN
which_irr(iclass)=set_e(has_e(1,iclass),8)
ELSEIF (ts==5) THEN
CALL mirror_axis(smat(1,1,elem(1,iclass)),ax)
IF (is_axis(ax,axis)) THEN
which_irr(iclass)=12
ELSE
IF (first1) THEN
which_irr(iclass)=13
first1=.FALSE.
ELSE
which_irr(iclass)=14
END IF
END IF
ELSEIF (ts==6) THEN
which_irr(iclass)=set_e(has_e(1,iclass),10)
END IF
END DO
ELSEIF (code_group==23) THEN
!
! D_6h
!
first=.TRUE.
first1=.TRUE.
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==1) THEN
which_irr(iclass)=2
ELSE IF (ts==3) THEN
ars=angle_rot(smat(1,1,elem(1,iclass)))
IF ((ABS(ars-60.d0)<eps).OR.(ABS(ars-300.d0)<eps)) THEN
which_irr(iclass)=set_e(has_e(1,iclass),6)
ELSE
which_irr(iclass)=set_e(has_e(1,iclass),4)
END IF
ELSE IF (ts==4) THEN
IF (nelem(iclass)==2) THEN
which_irr(iclass)=3
ELSE
IF (first) THEN
which_irr(iclass)=8
first=.FALSE.
ELSE
which_irr(iclass)=9
END IF
END IF
ELSE IF (ts==2) THEN
which_irr(iclass)=set_e(has_e(1,iclass),10)
ELSE IF (ts==5) THEN
IF (nelem(iclass)==2) THEN
which_irr(iclass)=12
ELSE
IF (first1) THEN
which_irr(iclass)=17
first1=.FALSE.
ELSE
which_irr(iclass)=18
ENDIF
END IF
ELSE IF (ts==6) THEN
ars=angle_rot_s(smat(1,1,elem(1,iclass)))
IF ((ABS(ars-60.d0)<eps).OR.(ABS(ars-300.d0)<eps)) THEN
which_irr(iclass)=set_e(has_e(1,iclass),13)
Bug fix. Bug reported in S_6 by Marino Vetuschi Zuccolini. Possible problems also in: S_4, S_6, T_h, C_3h, C_4h, C_6h. git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@5185 c92efa57-630b-4861-b058-cf58834340f0
2008-09-09 23:25:55 +08:00
ELSE
which_irr(iclass)=set_e(has_e(1,iclass),15)
Now bands.x can classify the bands according to the irreducible representation of the small group of k. k points on the border of the Brillouin zone of systems with non symmorphic space groups are not dealt with. Spin-orbit case included. Find_mode_sym extended to all the q points, with the same limitations as the bands. (still experimental). git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3330 c92efa57-630b-4861-b058-cf58834340f0
2006-08-23 01:01:13 +08:00
END IF
END IF
END DO
ELSEIF (code_group==24) THEN
!
! D_2d
!
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==1) THEN
which_irr(iclass)=2
ELSE IF (ts==6) THEN
which_irr(iclass)=set_e(has_e(1,iclass),4)
ELSE IF (ts==4) THEN
IF (nelem(iclass)==2) THEN
which_irr(iclass)=3
ELSE
which_irr(iclass)=6
END IF
ELSE IF (ts==5) THEN
which_irr(iclass)=7
ELSE
CALL errore('divide_class_so','wrong operation',1)
END IF
END DO
ELSEIF (code_group==25) THEN
!
! D_3d
!
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==1) THEN
which_irr(iclass)=2
ELSEIF (ts==3) THEN
which_irr(iclass)=set_e(has_e(1,iclass),3)
ELSE IF (ts==4) THEN
which_irr(iclass)=set_e(has_e(1,iclass),11)
ELSE IF (ts==2) THEN
which_irr(iclass)=set_e(has_e(1,iclass),7)
ELSE IF (ts==6) THEN
which_irr(iclass)=set_e(has_e(1,iclass),9)
ELSE IF (ts==5) THEN
which_irr(iclass)=set_e(has_e(1,iclass),5)
ELSE
CALL errore('divide_class_so','wrong operation',1)
END IF
END DO
ELSEIF (code_group==26) THEN
!
! S_4
!
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==1) THEN
which_irr(iclass)=2
ELSE IF (ts==4) THEN
which_irr(iclass)=set_e(has_e(1,iclass),5)
ELSE IF (ts==6) THEN
IF (ABS(angle_rot_s(smat(1,1,elem(1,iclass)))-90.d0)<eps) THEN
which_irr(iclass)=set_e(has_e(1,iclass),3)
ELSE
which_irr(iclass)=set_e(has_e(1,iclass),7)
END IF
ELSE
CALL errore('divide_class_so','wrong operation',1)
END IF
END DO
ELSE IF (code_group==27) THEN
!
! S_6
!
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==1) THEN
which_irr(iclass)=2
ELSE IF (ts==3) THEN
IF (ABS(angle_rot(smat(1,1,elem(1,iclass)))-120.d0)<eps) THEN
which_irr(iclass)=set_e(has_e(1,iclass),3)
ELSE
which_irr(iclass)=set_e(has_e(1,iclass),5)
END IF
ELSE IF (ts==2) THEN
which_irr(iclass)=set_e(has_e(1,iclass),7)
ELSE IF (ts==6) THEN
Bug fix. Bug reported in S_6 by Marino Vetuschi Zuccolini. Possible problems also in: S_4, S_6, T_h, C_3h, C_4h, C_6h. git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@5185 c92efa57-630b-4861-b058-cf58834340f0
2008-09-09 23:25:55 +08:00
IF (ABS(angle_rot_s(smat(1,1,elem(1,iclass)))-60.d0)<eps) THEN
Now bands.x can classify the bands according to the irreducible representation of the small group of k. k points on the border of the Brillouin zone of systems with non symmorphic space groups are not dealt with. Spin-orbit case included. Find_mode_sym extended to all the q points, with the same limitations as the bands. (still experimental). git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3330 c92efa57-630b-4861-b058-cf58834340f0
2006-08-23 01:01:13 +08:00
which_irr(iclass)=set_e(has_e(1,iclass),11)
ELSE
which_irr(iclass)=set_e(has_e(1,iclass),9)
END IF
ELSE
CALL errore('divide_class_so','wrong operation',1)
END IF
END DO
ELSEIF (code_group==28) THEN
!
! T
!
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==1) THEN
which_irr(iclass)=2
ELSE IF (ts==4) THEN
which_irr(iclass)=3
ELSE IF (ts==3) THEN
IF (ABS(angle_rot(smat(1,1,elem(1,iclass)))-120.d0)<eps) THEN
which_irr(iclass)=set_e(has_e(1,iclass),4)
ELSE IF (ABS(angle_rot(smat(1,1,elem(1,iclass)))-240.d0)<eps) THEN
which_irr(iclass)=set_e(has_e(1,iclass),6)
ENDIF
ELSE
CALL errore('divide_class_so','wrong sym type',1)
END IF
END DO
ELSE IF (code_group==29) THEN
!
! T_h
!
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==1) THEN
which_irr(iclass)=2
ELSE IF (ts==3) THEN
IF (ABS(angle_rot(smat(1,1,elem(1,iclass)))-120.d0)<eps) THEN
which_irr(iclass)=set_e(has_e(1,iclass),4)
ELSE
which_irr(iclass)=set_e(has_e(1,iclass),6)
END IF
ELSE IF (ts==4) THEN
which_irr(iclass)=3
ELSE IF (ts==2) THEN
which_irr(iclass)=set_e(has_e(1,iclass),8)
ELSE IF (ts==6) THEN
IF (ABS(angle_rot_s(smat(1,1,elem(1,iclass)))-60.d0)<eps) THEN
which_irr(iclass)=set_e(has_e(1,iclass),11)
ELSE
which_irr(iclass)=set_e(has_e(1,iclass),13)
END IF
ELSE IF (ts==5) THEN
which_irr(iclass)=10
ELSE
CALL errore('divide_class_so','wrong operation',1)
END IF
END DO
ELSEIF (code_group==30) THEN
!
! T_d
!
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==1) THEN
which_irr(iclass)=2
ELSE IF (ts==3) THEN
which_irr(iclass)=set_e(has_e(1,iclass),3)
ELSE IF (ts==4) THEN
which_irr(iclass)=5
ELSE IF (ts==6) THEN
which_irr(iclass)=set_e(has_e(1,iclass),7)
ELSE IF (ts==5) THEN
which_irr(iclass)=6
ELSE
CALL errore('divide_class_so','wrong operation',1)
END IF
END DO
ELSEIF (code_group==31) THEN
!
! O
!
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==1) THEN
which_irr(iclass)=2
ELSE IF (ts==4) THEN
which_irr(iclass)=set_e(has_e(1,iclass),6)
ELSE IF (ts==3) THEN
IF (nelem(iclass)==8) THEN
which_irr(iclass)=set_e(has_e(1,iclass),3)
ELSE
which_irr(iclass)=set_e(has_e(1,iclass),7)
END IF
ELSE
CALL errore('divide_class_so','wrong operation',1)
END IF
END DO
ELSEIF (code_group==32) THEN
!
! O_h
!
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==4) THEN
IF (nelem(iclass)==6) THEN
which_irr(iclass)=5
ELSE
which_irr(iclass)=8
END IF
ELSE IF (ts==3) THEN
IF (nelem(iclass)==8) THEN
which_irr(iclass)=set_e(has_e(1,iclass),3)
ELSE
which_irr(iclass)=set_e(has_e(1,iclass),6)
END IF
ELSE IF (ts==2) THEN
which_irr(iclass)=set_e(has_e(1,iclass),9)
ELSE IF (ts==5) THEN
IF (nelem(iclass)==12) THEN
which_irr(iclass)=16
ELSE
which_irr(iclass)=13
END IF
ELSE IF (ts==6) THEN
IF (nelem(iclass)==8) THEN
which_irr(iclass)=set_e(has_e(1,iclass),11)
ELSE
which_irr(iclass)=set_e(has_e(1,iclass),14)
END IF
ELSE IF (ts==1) THEN
which_irr(iclass)=2
ELSE
CALL errore('divide_class','wrong operation',1)
END IF
ENDDO
ELSE
CALL errore('divide_class_so','code_group not correct',1)
ENDIF
RETURN
END SUBROUTINE divide_class_so
!-----------------------------------------------------------------------------
SUBROUTINE coniug_mat_so(a,a_spin,b,b_spin,c,c_spin)
!-----------------------------------------------------------------------------
USE kinds, ONLY : DP
IMPLICIT NONE
REAL(DP) :: a(3,3), b(3,3), c(3,3)
COMPLEX(DP) :: a_spin(2,2), b_spin(2,2), c_spin(2,2)
c=MATMUL(a,MATMUL(b,TRANSPOSE(a)))
c_spin=MATMUL(a_spin,MATMUL(b_spin,TRANSPOSE(CONJG(a_spin))))
RETURN
END SUBROUTINE coniug_mat_so
!
!-----------------------------------------------------------------------------
FUNCTION compare_mat_so(a,a_spin,b,b_spin)
!-----------------------------------------------------------------------------
!
! This function compare two 3x3 matrices and two 2x2 matrices
! and returns .true. if they coincide.
!
USE kinds, ONLY : DP
IMPLICIT NONE
REAL(DP) :: a(3,3), b(3,3), csum
REAL(DP), PARAMETER :: eps=1.d-7
COMPLEX(DP) :: a_spin(2,2), b_spin(2,2)
LOGICAL :: compare_mat_so
INTEGER :: i, j
csum=0.d0
DO i=1,2
DO j=1,2
csum=csum+ABS(a_spin(i,j)-b_spin(i,j))
END DO
END DO
compare_mat_so=((ABS(MAXVAL(a-b))<eps).AND. &
(ABS(MINVAL(a-b))<eps).AND. (csum < eps ))
RETURN
END FUNCTION compare_mat_so
!-----------------------------------------------------------------------------
SUBROUTINE set_irr_rap_so(code_group,nclass_ref,nrap_ref,char_mat,&
name_rap,name_class,name_class1)
!-----------------------------------------------------------------------------
!
! This subroutine collects the character tables of the 32 crystallographic
! double point groups. Various names have been used in the litterature
! to identify D, G, L, S are used for Delta, Gamma, Lambda and Sigma.
!
!
USE kinds, ONLY : DP
IMPLICIT NONE
INTEGER :: nclass_ref, & ! Output: number of classes
nrap_ref, & ! Output: number of irreducible representation
code_group ! Input: code of the group
CHARACTER(LEN=15) :: name_rap(24) ! Output: name of the representations
CHARACTER(LEN=5) :: name_class(24), & ! Output: name of the classes
name_class1(24) ! Output: name of the classes
COMPLEX(DP) :: char_mat(12,24) ! Output: character matrix
REAL(DP) :: sqr3d2, sqrt2, sqrt3, dsq2
sqrt2 =SQRT(2.d0)
sqrt3 =SQRT(3.d0)
sqr3d2=sqrt3*0.5d0
dsq2 =sqrt2*0.5d0
char_mat=(1.d0,0.d0)
char_mat(:,2)=(-1.d0,0.d0)
name_class1=" "
name_class(1)="E "
name_class(2)="-E "
IF (code_group==1) THEN
!
! C_1
!
nclass_ref=2
nrap_ref=1
name_rap(1)="G_2 "
ELSEIF (code_group==2) THEN
!
! C_i
!
nclass_ref=4
name_class(3)="i "
name_class(4)="-i "
nrap_ref=2
name_rap(1)="G_2+"
char_mat(1,4)=(-1.d0,0.d0)
name_rap(2)="G_2-"
char_mat(2,3)=(-1.d0,0.d0)
ELSEIF (code_group==3) THEN
!
! C_s
!
nclass_ref=4
name_class(3)="s "
name_class(4)="-s "
nrap_ref=2
name_rap(1)="G_3 "
char_mat(1,3)=(0.d0, 1.d0)
char_mat(1,4)=(0.d0,-1.d0)
name_rap(2)="G_4 "
char_mat(2,3)=(0.d0,-1.d0)
char_mat(2,4)=(0.d0, 1.d0)
ELSEIF (code_group==4) THEN
!
! C_2
!
nclass_ref=4
name_class(3)="C2 "
name_class(4)="-C2 "
nrap_ref=2
name_rap(1)="G_3 "
char_mat(1,3)=(0.d0, 1.d0)
char_mat(1,4)=(0.d0,-1.d0)
name_rap(2)="G_4 "
char_mat(2,3)=(0.d0,-1.d0)
char_mat(2,4)=(0.d0, 1.d0)
ELSEIF (code_group==5) THEN
!
! C_3
!
nclass_ref=6
name_class(3)="C3 "
name_class(4)="-C3 "
name_class(5)="C3^2 "
name_class(6)="-C3^2"
nrap_ref=3
name_rap(1)="G_4 "
char_mat(1,3)=CMPLX( 0.5d0, sqr3d2)
char_mat(1,4)=CMPLX(-0.5d0,-sqr3d2)
char_mat(1,5)=CMPLX(-0.5d0, sqr3d2)
char_mat(1,6)=CMPLX( 0.5d0,-sqr3d2)
name_rap(2)="G_5 "
char_mat(2,3)=CMPLX( 0.5d0,-sqr3d2)
char_mat(2,4)=CMPLX(-0.5d0, sqr3d2)
char_mat(2,5)=CMPLX(-0.5d0,-sqr3d2)
char_mat(2,6)=CMPLX( 0.5d0, sqr3d2)
name_rap(3)="G_6 "
char_mat(3,3)=(-1.0d0,0.d0)
char_mat(3,6)=(-1.0d0,0.d0)
ELSEIF (code_group==6) THEN
!
Problems with the C_4 character table. Updated output in sym_band.f90. git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3341 c92efa57-630b-4861-b058-cf58834340f0
2006-08-25 16:19:55 +08:00
! C_4 NB: The signs of the characters of the class C4^3 -C4^2
! are changed with respect to Koster, Space groups and
! their representation.
Now bands.x can classify the bands according to the irreducible representation of the small group of k. k points on the border of the Brillouin zone of systems with non symmorphic space groups are not dealt with. Spin-orbit case included. Find_mode_sym extended to all the q points, with the same limitations as the bands. (still experimental). git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3330 c92efa57-630b-4861-b058-cf58834340f0
2006-08-23 01:01:13 +08:00
!
nclass_ref=8
name_class(3)="C4 "
name_class(4)="-C4 "
name_class(5)="C4^2 "
name_class(6)="-C4^2 "
name_class(7)="C4^3 "
name_class(8)="-C4^3 "
nrap_ref=4
name_rap(1)="G_5 "
char_mat(1,3)=CMPLX( dsq2, dsq2)
char_mat(1,4)=CMPLX(-dsq2,-dsq2)
char_mat(1,5)=( 0.d0,1.d0)
char_mat(1,6)=( 0.d0,-1.d0)
Problems with the C_4 character table. Updated output in sym_band.f90. git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3341 c92efa57-630b-4861-b058-cf58834340f0
2006-08-25 16:19:55 +08:00
! char_mat(1,7)=CMPLX(-dsq2, dsq2)
! char_mat(1,8)=CMPLX( dsq2,-dsq2)
char_mat(1,7)=CMPLX( dsq2,-dsq2)
char_mat(1,8)=CMPLX(-dsq2, dsq2)
Now bands.x can classify the bands according to the irreducible representation of the small group of k. k points on the border of the Brillouin zone of systems with non symmorphic space groups are not dealt with. Spin-orbit case included. Find_mode_sym extended to all the q points, with the same limitations as the bands. (still experimental). git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3330 c92efa57-630b-4861-b058-cf58834340f0
2006-08-23 01:01:13 +08:00
name_rap(2)="G_6 "
char_mat(2,3)=CMPLX( dsq2,-dsq2)
char_mat(2,4)=CMPLX(-dsq2, dsq2)
char_mat(2,5)=( 0.d0,-1.d0)
char_mat(2,6)=( 0.d0, 1.d0)
Problems with the C_4 character table. Updated output in sym_band.f90. git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3341 c92efa57-630b-4861-b058-cf58834340f0
2006-08-25 16:19:55 +08:00
! char_mat(2,7)=CMPLX(-dsq2,-dsq2)
! char_mat(2,8)=CMPLX( dsq2, dsq2)
char_mat(2,7)=CMPLX( dsq2, dsq2)
char_mat(2,8)=CMPLX(-dsq2,-dsq2)
Now bands.x can classify the bands according to the irreducible representation of the small group of k. k points on the border of the Brillouin zone of systems with non symmorphic space groups are not dealt with. Spin-orbit case included. Find_mode_sym extended to all the q points, with the same limitations as the bands. (still experimental). git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3330 c92efa57-630b-4861-b058-cf58834340f0
2006-08-23 01:01:13 +08:00
name_rap(3)="G_7 "
char_mat(3,3)=CMPLX(-dsq2,-dsq2)
char_mat(3,4)=CMPLX( dsq2, dsq2)
char_mat(3,5)=( 0.d0,1.d0)
char_mat(3,6)=( 0.d0,-1.d0)
Problems with the C_4 character table. Updated output in sym_band.f90. git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3341 c92efa57-630b-4861-b058-cf58834340f0
2006-08-25 16:19:55 +08:00
! char_mat(3,7)=CMPLX( dsq2,-dsq2)
! char_mat(3,8)=CMPLX(-dsq2, dsq2)
char_mat(3,7)=CMPLX(-dsq2, dsq2)
char_mat(3,8)=CMPLX( dsq2,-dsq2)
Now bands.x can classify the bands according to the irreducible representation of the small group of k. k points on the border of the Brillouin zone of systems with non symmorphic space groups are not dealt with. Spin-orbit case included. Find_mode_sym extended to all the q points, with the same limitations as the bands. (still experimental). git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3330 c92efa57-630b-4861-b058-cf58834340f0
2006-08-23 01:01:13 +08:00
name_rap(4)="G_8 "
char_mat(4,3)=CMPLX(-dsq2, dsq2)
char_mat(4,4)=CMPLX( dsq2,-dsq2)
char_mat(4,5)=( 0.d0,-1.d0)
char_mat(4,6)=( 0.d0, 1.d0)
Problems with the C_4 character table. Updated output in sym_band.f90. git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3341 c92efa57-630b-4861-b058-cf58834340f0
2006-08-25 16:19:55 +08:00
! char_mat(4,7)=CMPLX( dsq2, dsq2)
! char_mat(4,8)=CMPLX(-dsq2,-dsq2)
char_mat(4,7)=CMPLX(-dsq2,-dsq2)
char_mat(4,8)=CMPLX( dsq2, dsq2)
Now bands.x can classify the bands according to the irreducible representation of the small group of k. k points on the border of the Brillouin zone of systems with non symmorphic space groups are not dealt with. Spin-orbit case included. Find_mode_sym extended to all the q points, with the same limitations as the bands. (still experimental). git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3330 c92efa57-630b-4861-b058-cf58834340f0
2006-08-23 01:01:13 +08:00
ELSEIF (code_group==7) THEN
!
! C_6 NB: The signs of characters of the C3^2 -C3^2 C6^5 -C6^5 classes
! are changed with respect to Koster, Space groups and their
! representation. They match the table in Koster, Dimmok,
! Wheeler, Statz, Properties of the 32 point groups.
!
nclass_ref=12
name_class(3)="C6 "
name_class(4)="-C6 "
name_class(5)="C3 "
name_class(6)="-C3 "
name_class(7)="C2 "
name_class(8)="-C2 "
name_class(9)="C3^2"
name_class(10)="-C3^2"
name_class(11)="C6^5"
name_class(12)="-C6^5"
nrap_ref=6
name_rap(1)="G_7 "
char_mat(1,2)=(-1.d0, 0.d0)
char_mat(1,3)=CMPLX( sqr3d2, 0.5d0)
char_mat(1,4)=CMPLX(-sqr3d2,-0.5d0)
char_mat(1,5)=CMPLX( 0.5d0, sqr3d2)
char_mat(1,6)=CMPLX(-0.5d0,-sqr3d2)
char_mat(1,7)=( 0.d0, 1.d0)
char_mat(1,8)=( 0.d0,-1.d0)
! char_mat(1,9)=CMPLX(-0.5d0, sqr3d2)
! char_mat(1,10)=CMPLX( 0.5d0,-sqr3d2)
! char_mat(1,11)=CMPLX(-sqr3d2, 0.5d0)
! char_mat(1,12)=CMPLX( sqr3d2,-0.5d0)
char_mat(1,9)=CMPLX( 0.5d0,-sqr3d2)
char_mat(1,10)=CMPLX(-0.5d0, sqr3d2)
char_mat(1,11)=CMPLX( sqr3d2,-0.5d0)
char_mat(1,12)=CMPLX(-sqr3d2, 0.5d0)
name_rap(2)="G_8 "
char_mat(2,2)=(-1.d0, 0.d0)
char_mat(2,3)=CMPLX( sqr3d2,-0.5d0)
char_mat(2,4)=CMPLX(-sqr3d2, 0.5d0)
char_mat(2,5)=CMPLX( 0.5d0,-sqr3d2)
char_mat(2,6)=CMPLX(-0.5d0, sqr3d2)
char_mat(2,7)=( 0.d0,-1.d0)
char_mat(2,8)=( 0.d0, 1.d0)
! char_mat(2,9)=CMPLX(-0.5d0,-sqr3d2)
! char_mat(2,10)=CMPLX( 0.5d0, sqr3d2)
! char_mat(2,11)=CMPLX(-sqr3d2,-0.5d0)
! char_mat(2,12)=CMPLX( sqr3d2, 0.5d0)
char_mat(2,9)=CMPLX( 0.5d0, sqr3d2)
char_mat(2,10)=CMPLX(-0.5d0,-sqr3d2)
char_mat(2,11)=CMPLX( sqr3d2, 0.5d0)
char_mat(2,12)=CMPLX(-sqr3d2,-0.5d0)
name_rap(3)="G_11 "
char_mat(3,2)=(-1.d0, 0.d0)
char_mat(3,3)=( 0.d0, 1.d0)
char_mat(3,4)=( 0.d0,-1.d0)
char_mat(3,5)=(-1.d0, 0.d0)
char_mat(3,7)=( 0.d0,-1.d0)
char_mat(3,8)=( 0.d0, 1.d0)
! char_mat(3,10)=(-1.d0, 0.d0)
! char_mat(3,11)=( 0.d0, 1.d0)
! char_mat(3,12)=( 0.d0,-1.d0)
char_mat(3,9)=(-1.d0, 0.d0)
char_mat(3,11)=( 0.d0,-1.d0)
char_mat(3,12)=( 0.d0, 1.d0)
name_rap(4)="G_12 "
char_mat(4,2)=(-1.d0, 0.d0)
char_mat(4,3)=( 0.d0,-1.d0)
char_mat(4,4)=( 0.d0, 1.d0)
char_mat(4,5)=(-1.d0, 0.d0)
char_mat(4,7)=( 0.d0, 1.d0)
char_mat(4,8)=( 0.d0,-1.d0)
! char_mat(4,10)=(-1.d0, 0.d0)
! char_mat(4,11)=( 0.d0,-1.d0)
! char_mat(4,12)=( 0.d0, 1.d0)
char_mat(4,9)=(-1.d0, 0.d0)
char_mat(4,11)=( 0.d0, 1.d0)
char_mat(4,12)=( 0.d0,-1.d0)
name_rap(5)="G_9 "
char_mat(5,2)=(-1.d0, 0.d0)
char_mat(5,3)=CMPLX(-sqr3d2,-0.5d0)
char_mat(5,4)=CMPLX( sqr3d2, 0.5d0)
char_mat(5,5)=CMPLX( 0.5d0, sqr3d2)
char_mat(5,6)=CMPLX(-0.5d0,-sqr3d2)
char_mat(5,7)=( 0.d0,-1.d0)
char_mat(5,8)=( 0.d0, 1.d0)
! char_mat(5,9)=CMPLX(-0.5d0, sqr3d2)
! char_mat(5,10)=CMPLX( 0.5d0,-sqr3d2)
! char_mat(5,11)=CMPLX( sqr3d2,-0.5d0)
! char_mat(5,12)=CMPLX(-sqr3d2, 0.5d0)
char_mat(5,9)=CMPLX( 0.5d0,-sqr3d2)
char_mat(5,10)=CMPLX(-0.5d0, sqr3d2)
char_mat(5,11)=CMPLX(-sqr3d2, 0.5d0)
char_mat(5,12)=CMPLX( sqr3d2,-0.5d0)
name_rap(6)="G_10 "
char_mat(6,2)=(-1.d0, 0.d0)
char_mat(6,3)=CMPLX(-sqr3d2, 0.5d0)
char_mat(6,4)=CMPLX( sqr3d2,-0.5d0)
char_mat(6,5)=CMPLX( 0.5d0,-sqr3d2)
char_mat(6,6)=CMPLX(-0.5d0, sqr3d2)
char_mat(6,7)=( 0.d0, 1.d0)
char_mat(6,8)=( 0.d0,-1.d0)
! char_mat(6,9)=CMPLX(-0.5d0,-sqr3d2)
! char_mat(6,10)=CMPLX( 0.5d0, sqr3d2)
! char_mat(6,11)=CMPLX( sqr3d2, 0.5d0)
! char_mat(6,12)=CMPLX(-sqr3d2,-0.5d0)
char_mat(6,9)=CMPLX( 0.5d0, sqr3d2)
char_mat(6,10)=CMPLX(-0.5d0,-sqr3d2)
char_mat(6,11)=CMPLX(-sqr3d2,-0.5d0)
char_mat(6,12)=CMPLX( sqr3d2, 0.5d0)
ELSEIF (code_group==8) THEN
!
! D_2
!
nclass_ref=5
name_class(3)="C2 "
name_class1(3)="-C2 "
name_class(4)="C2' "
name_class1(4)="-C2' "
name_class(5)="C2''"
name_class1(5)="-C2''"
nrap_ref=1
name_rap(1)="G_5 "
char_mat(1,1)=( 2.d0, 0.d0)
char_mat(1,2)=(-2.d0, 0.d0)
char_mat(1,3)=( 0.d0, 0.d0)
char_mat(1,4)=( 0.d0, 0.d0)
char_mat(1,5)=( 0.d0, 0.d0)
ELSEIF (code_group==9) THEN
!
! D_3
!
nclass_ref=6
name_class(3)="2C3 "
name_class(4)="-2C3 "
name_class(5)=" 3C2'"
name_class(6)="-3C2'"
nrap_ref=3
name_rap(1)="G_4 "
char_mat(1,1)=( 2.d0, 0.d0)
char_mat(1,2)=(-2.d0, 0.d0)
char_mat(1,4)=(-1.d0, 0.d0)
char_mat(1,5)=( 0.d0, 0.d0)
char_mat(1,6)=( 0.d0, 0.d0)
name_rap(2)="G_5 "
char_mat(2,2)=(-1.d0, 0.d0)
char_mat(2,3)=(-1.d0, 0.d0)
char_mat(2,5)=( 0.d0, 1.d0)
char_mat(2,6)=( 0.d0,-1.d0)
name_rap(3)="G_6 "
char_mat(3,2)=(-1.d0, 0.d0)
char_mat(3,3)=(-1.d0, 0.d0)
char_mat(3,5)=( 0.d0,-1.d0)
char_mat(3,6)=( 0.d0, 1.d0)
ELSEIF (code_group==10) THEN
!
! D_4
!
nclass_ref=7
name_class(3)="2C4 "
name_class(4)="-2C4 "
name_class(5)=" C2 "
name_class1(5)="-C2 "
name_class(6)="2C2'"
name_class1(6)="-2C2'"
name_class(7)="2C2'' "
name_class1(7)="-2C2''"
nrap_ref=2
name_rap(1)="G_6 "
char_mat(1,1)=( 2.d0, 0.d0)
char_mat(1,2)=(-2.d0, 0.d0)
char_mat(1,3)=CMPLX( sqrt2, 0.d0)
char_mat(1,4)=CMPLX(-sqrt2, 0.d0)
char_mat(1,5)=( 0.d0, 0.d0)
char_mat(1,6)=( 0.d0, 0.d0)
char_mat(1,7)=( 0.d0, 0.d0)
name_rap(2)="G_7 "
char_mat(2,1)=( 2.d0, 0.d0)
char_mat(2,2)=(-2.d0, 0.d0)
char_mat(2,3)=CMPLX(-sqrt2, 0.d0)
char_mat(2,4)=CMPLX( sqrt2, 0.d0)
char_mat(2,5)=( 0.d0, 0.d0)
char_mat(2,6)=( 0.d0, 0.d0)
char_mat(2,7)=( 0.d0, 0.d0)
ELSEIF (code_group==12) THEN
!
! C_2v
!
nclass_ref=5
name_class(3)=" C2"
name_class1(3)="-C2"
name_class(4)=" s_v"
name_class1(4)="-s_v"
name_class(5)=" s_v'"
name_class1(5)="-s_v'"
nrap_ref=1
name_rap(1)="G_5 D_5"
char_mat(1,1)=( 2.d0, 0.d0)
char_mat(1,2)=(-2.d0, 0.d0)
char_mat(1,3)=( 0.d0, 0.d0)
char_mat(1,4)=( 0.d0, 0.d0)
char_mat(1,5)=( 0.d0, 0.d0)
ELSEIF (code_group==13) THEN
!
! C_3v
!
nclass_ref=6
name_class(3)="2C3 "
name_class(4)="-2C3 "
name_class(5)="3s_v"
name_class(6)="-3s_v"
nrap_ref=3
name_rap(1)="G_4 L_6 "
char_mat(1,1)=( 2.d0, 0.d0)
char_mat(1,2)=(-2.d0, 0.d0)
char_mat(1,4)=(-1.d0, 0.d0)
char_mat(1,5)=( 0.d0, 0.d0)
char_mat(1,6)=( 0.d0, 0.d0)
name_rap(2)="G_5 L_4 "
char_mat(2,3)=(-1.d0, 0.d0)
char_mat(2,5)=( 0.d0, 1.d0)
char_mat(2,6)=( 0.d0,-1.d0)
name_rap(3)="G_6 L_5 "
char_mat(3,3)=(-1.d0, 0.d0)
char_mat(3,5)=( 0.d0,-1.d0)
char_mat(3,6)=( 0.d0, 1.d0)
ELSEIF (code_group==14) THEN
!
! C_4v
!
nclass_ref=7
name_class(3)="2C4 "
name_class(4)="-2C4 "
name_class(5)=" C2"
name_class1(5)="-C2"
name_class(6)=" 2s_v"
name_class1(6)="-2s_v"
name_class(7)=" 2s_d"
name_class1(7)="-2s_d"
nrap_ref=2
name_rap(1)="G_6 D_6"
char_mat(1,1)=( 2.d0, 0.d0)
char_mat(1,2)=(-2.d0, 0.d0)
char_mat(1,3)=CMPLX( sqrt2, 0.d0)
char_mat(1,4)=CMPLX(-sqrt2, 0.d0)
char_mat(1,5)=( 0.d0, 0.d0)
char_mat(1,6)=( 0.d0, 0.d0)
char_mat(1,7)=( 0.d0, 0.d0)
name_rap(2)="G_7 D_7"
char_mat(2,1)=( 2.d0, 0.d0)
char_mat(2,2)=(-2.d0, 0.d0)
char_mat(2,3)=CMPLX(-sqrt2, 0.d0)
char_mat(2,4)=CMPLX( sqrt2, 0.d0)
char_mat(2,5)=( 0.d0, 0.d0)
char_mat(2,6)=( 0.d0, 0.d0)
char_mat(2,7)=( 0.d0, 0.d0)
ELSEIF (code_group==15.OR.code_group==11) THEN
!
! C_6v, D_6
!
nclass_ref=9
name_class(3)=" C2 "
name_class1(3)="-C2 "
name_class(4)=" 2C3 "
name_class(5)="-2C3"
name_class(6)=" 2C6"
name_class(7)="-2C6"
IF (code_group==15) THEN
name_class(8)=" 3s_v"
name_class1(8)="-3s_v"
name_class(9)=" 3s_d"
name_class1(9)="-3s_d"
ELSE
name_class(8)=" 3C2'"
name_class1(8)="-3C2'"
name_class(9)="3C2''"
name_class1(9)="-3C2''"
END IF
nrap_ref=3
name_rap(1)="G_7 "
char_mat(1,1)=( 2.d0, 0.d0)
char_mat(1,2)=(-2.d0, 0.d0)
char_mat(1,3)=( 0.d0, 0.d0)
char_mat(1,5)=(-1.d0, 0.d0)
char_mat(1,6)=CMPLX( sqrt3, 0.d0)
char_mat(1,7)=CMPLX(-sqrt3, 0.d0)
char_mat(1,8)=( 0.d0, 0.d0)
char_mat(1,9)=( 0.d0, 0.d0)
name_rap(2)="G_8 "
char_mat(2,1)=( 2.d0, 0.d0)
char_mat(2,2)=(-2.d0, 0.d0)
char_mat(2,3)=( 0.d0, 0.d0)
char_mat(2,5)=(-1.d0, 0.d0)
char_mat(2,6)=CMPLX(-sqrt3, 0.d0)
char_mat(2,7)=CMPLX( sqrt3, 0.d0)
char_mat(2,8)=( 0.d0, 0.d0)
char_mat(2,9)=( 0.d0, 0.d0)
name_rap(3)="G_9 "
char_mat(3,1)=( 2.d0, 0.d0)
char_mat(3,2)=(-2.d0, 0.d0)
char_mat(3,3)=( 0.d0, 0.d0)
char_mat(3,4)=(-2.d0, 0.d0)
char_mat(3,5)=( 2.d0, 0.d0)
char_mat(3,6)=( 0.d0, 0.d0)
char_mat(3,7)=( 0.d0, 0.d0)
char_mat(3,8)=( 0.d0, 0.d0)
char_mat(3,9)=( 0.d0, 0.d0)
ELSEIF (code_group==16) THEN
!
! C_2h
!
nclass_ref=8
name_class(3)="C2 "
name_class(4)="-C2 "
name_class(5)="s_h "
name_class(6)="-s_h"
name_class(7)="i "
name_class(8)="-i "
nrap_ref=4
name_rap(1)="G_3+"
char_mat(1,3)=( 0.d0, 1.d0)
char_mat(1,4)=( 0.d0,-1.d0)
char_mat(1,5)=( 0.d0, 1.d0)
char_mat(1,6)=( 0.d0,-1.d0)
char_mat(1,8)=(-1.d0, 0.d0)
name_rap(2)="G_4+"
char_mat(2,3)=( 0.d0,-1.d0)
char_mat(2,4)=( 0.d0, 1.d0)
char_mat(2,5)=( 0.d0,-1.d0)
char_mat(2,6)=( 0.d0, 1.d0)
char_mat(2,8)=(-1.d0, 0.d0)
name_rap(3)="G_3-"
char_mat(3,3)=( 0.d0, 1.d0)
char_mat(3,4)=( 0.d0,-1.d0)
char_mat(3,5)=( 0.d0,-1.d0)
char_mat(3,6)=( 0.d0, 1.d0)
char_mat(3,7)=(-1.d0, 0.d0)
name_rap(4)="G_4- "
char_mat(4,3)=( 0.d0,-1.d0)
char_mat(4,4)=( 0.d0, 1.d0)
char_mat(4,5)=( 0.d0, 1.d0)
char_mat(4,6)=( 0.d0,-1.d0)
char_mat(4,7)=(-1.d0, 0.d0)
ELSEIF (code_group==17) THEN
!
! C_3h
!
nclass_ref=12
name_class(3)="C3 "
name_class(4)="-C3 "
name_class(5)="C3^2"
name_class(6)="-C3^2"
name_class(7)=" s_h "
name_class(8)="-s_h "
name_class(9)=" S3 "
name_class(10)="-S3 "
name_class(11)=" S3^5"
name_class(12)="-S3^5"
nrap_ref=6
name_rap(1)="G_7 "
char_mat(1,2)=(-1.d0, 0.d0)
char_mat(1,3)=CMPLX( 0.5d0, sqr3d2)
char_mat(1,4)=CMPLX(-0.5d0,-sqr3d2)
char_mat(1,5)=CMPLX(-0.5d0, sqr3d2)
char_mat(1,6)=CMPLX( 0.5d0,-sqr3d2)
char_mat(1,7)=( 0.d0, 1.d0)
char_mat(1,8)=( 0.d0,-1.d0)
char_mat(1,9)= CMPLX(-sqr3d2, 0.5d0)
char_mat(1,10)=CMPLX( sqr3d2,-0.5d0)
char_mat(1,11)=CMPLX( sqr3d2, 0.5d0)
char_mat(1,12)=CMPLX(-sqr3d2,-0.5d0)
name_rap(2)="G_8 "
char_mat(2,2)=(-1.d0, 0.d0)
char_mat(2,3)=CMPLX( 0.5d0,-sqr3d2)
char_mat(2,4)=CMPLX(-0.5d0, sqr3d2)
char_mat(2,5)=CMPLX(-0.5d0,-sqr3d2)
char_mat(2,6)=CMPLX( 0.5d0, sqr3d2)
char_mat(2,7)=( 0.d0,-1.d0)
char_mat(2,8)=( 0.d0, 1.d0)
char_mat(2,9)= CMPLX(-sqr3d2,-0.5d0)
char_mat(2,10)=CMPLX( sqr3d2, 0.5d0)
char_mat(2,11)=CMPLX( sqr3d2,-0.5d0)
char_mat(2,12)=CMPLX(-sqr3d2, 0.5d0)
name_rap(3)="G_9 "
char_mat(3,2)=(-1.d0, 0.d0)
char_mat(3,3)=CMPLX( 0.5d0, sqr3d2)
char_mat(3,4)=CMPLX(-0.5d0,-sqr3d2)
char_mat(3,5)=CMPLX(-0.5d0, sqr3d2)
char_mat(3,6)=CMPLX( 0.5d0,-sqr3d2)
char_mat(3,7)=( 0.d0,-1.d0)
char_mat(3,8)=( 0.d0, 1.d0)
char_mat(3,9)= CMPLX( sqr3d2,-0.5d0)
char_mat(3,10)=CMPLX(-sqr3d2, 0.5d0)
char_mat(3,11)=CMPLX(-sqr3d2,-0.5d0)
char_mat(3,12)=CMPLX( sqr3d2, 0.5d0)
name_rap(4)="G_10 "
char_mat(4,2)=(-1.d0, 0.d0)
char_mat(4,3)=CMPLX( 0.5d0,-sqr3d2)
char_mat(4,4)=CMPLX(-0.5d0, sqr3d2)
char_mat(4,5)=CMPLX(-0.5d0,-sqr3d2)
char_mat(4,6)=CMPLX( 0.5d0, sqr3d2)
char_mat(4,7)=( 0.d0, 1.d0)
char_mat(4,8)=( 0.d0,-1.d0)
char_mat(4,9)= CMPLX( sqr3d2, 0.5d0)
char_mat(4,10)=CMPLX(-sqr3d2,-0.5d0)
char_mat(4,11)=CMPLX(-sqr3d2, 0.5d0)
char_mat(4,12)=CMPLX( sqr3d2,-0.5d0)
name_rap(5)="G_11 "
char_mat(5,2)=(-1.d0, 0.d0)
char_mat(5,3)=(-1.d0, 0.d0)
char_mat(5,6)=(-1.d0, 0.d0)
char_mat(5,7)=( 0.d0, 1.d0)
char_mat(5,8)=( 0.d0,-1.d0)
char_mat(5,9)=( 0.d0,-1.d0)
char_mat(5,10)=( 0.d0, 1.d0)
char_mat(5,11)=( 0.d0,-1.d0)
char_mat(5,12)=( 0.d0, 1.d0)
name_rap(6)="G_12 "
char_mat(6,2)=(-1.d0, 0.d0)
char_mat(6,3)=(-1.d0, 0.d0)
char_mat(6,6)=(-1.d0, 0.d0)
char_mat(6,7)=( 0.d0,-1.d0)
char_mat(6,8)=( 0.d0, 1.d0)
char_mat(6,9)=( 0.d0, 1.d0)
char_mat(6,10)=( 0.d0,-1.d0)
char_mat(6,11)=( 0.d0, 1.d0)
char_mat(6,12)=( 0.d0,-1.d0)
ELSEIF (code_group==18) THEN
!
! C_4h NB: The signs of the characters of the class C4^3 -C4^2 S4 -S4
! are changed with respect to Koster, Space groups and
! their representation. They match the table in Koster,
! Dimmok, Wheeler, Statz, Properties of the 32 point groups.
!
nclass_ref=16
name_class(3)="C4 "
name_class(4)="-C4 "
name_class(5)="C4^2"
name_class(6)="-C4^2"
name_class(7)="C4^3"
name_class(8)="-C4^3"
name_class(9)="i "
name_class(10)="-i "
name_class(11)="S4^3"
name_class(12)="-S4^3"
name_class(13)="s_h "
name_class(14)="-s_h"
name_class(15)="S4 "
name_class(16)="-S4"
nrap_ref=8
name_rap(1)="G_5+ "
char_mat(1,3)=CMPLX( dsq2, dsq2)
char_mat(1,4)=CMPLX(-dsq2,-dsq2)
char_mat(1,5)=( 0.d0, 1.d0)
char_mat(1,6)=( 0.d0,-1.d0)
char_mat(1,7)=CMPLX( dsq2,-dsq2)
char_mat(1,8)=CMPLX(-dsq2, dsq2)
char_mat(1,10)=(-1.d0, 0.d0)
char_mat(1,11)=CMPLX( dsq2, dsq2)
char_mat(1,12)=CMPLX(-dsq2,-dsq2)
char_mat(1,13)=( 0.d0, 1.d0)
char_mat(1,14)=( 0.d0,-1.d0)
char_mat(1,15)=CMPLX( dsq2,-dsq2)
char_mat(1,16)=CMPLX(-dsq2, dsq2)
name_rap(2)="G_6+ "
char_mat(2,3)=CMPLX( dsq2,-dsq2)
char_mat(2,4)=CMPLX(-dsq2, dsq2)
char_mat(2,5)=( 0.d0,-1.d0)
char_mat(2,6)=( 0.d0, 1.d0)
char_mat(2,7)=CMPLX( dsq2, dsq2)
char_mat(2,8)=CMPLX(-dsq2,-dsq2)
char_mat(2,10)=(-1.d0, 0.d0)
char_mat(2,11)=CMPLX( dsq2,-dsq2)
char_mat(2,12)=CMPLX(-dsq2, dsq2)
char_mat(2,13)=( 0.d0,-1.d0)
char_mat(2,14)=( 0.d0, 1.d0)
char_mat(2,15)=CMPLX( dsq2, dsq2)
char_mat(2,16)=CMPLX(-dsq2,-dsq2)
name_rap(3)="G_7+ "
char_mat(3,3)=CMPLX(-dsq2,-dsq2)
char_mat(3,4)=CMPLX( dsq2, dsq2)
char_mat(3,5)=( 0.d0, 1.d0)
char_mat(3,6)=( 0.d0,-1.d0)
char_mat(3,7)=CMPLX(-dsq2, dsq2)
char_mat(3,8)=CMPLX( dsq2,-dsq2)
char_mat(3,10)=(-1.d0, 0.d0)
char_mat(3,11)=CMPLX(-dsq2,-dsq2)
char_mat(3,12)=CMPLX( dsq2, dsq2)
char_mat(3,13)=( 0.d0, 1.d0)
char_mat(3,14)=( 0.d0,-1.d0)
char_mat(3,15)=CMPLX(-dsq2, dsq2)
char_mat(3,16)=CMPLX( dsq2,-dsq2)
name_rap(4)="G_8+ "
char_mat(4,3)=CMPLX(-dsq2, dsq2)
char_mat(4,4)=CMPLX( dsq2,-dsq2)
char_mat(4,5)=( 0.d0,-1.d0)
char_mat(4,6)=( 0.d0, 1.d0)
char_mat(4,7)=CMPLX(-dsq2,-dsq2)
char_mat(4,8)=CMPLX( dsq2, dsq2)
char_mat(4,10)=(-1.d0, 0.d0)
char_mat(4,11)=CMPLX(-dsq2, dsq2)
char_mat(4,12)=CMPLX( dsq2,-dsq2)
char_mat(4,13)=( 0.d0,-1.d0)
char_mat(4,14)=( 0.d0, 1.d0)
char_mat(4,15)=CMPLX(-dsq2,-dsq2)
char_mat(4,16)=CMPLX( dsq2, dsq2)
name_rap(5)="G_5- "
char_mat(5,3)=CMPLX( dsq2, dsq2)
char_mat(5,4)=CMPLX(-dsq2,-dsq2)
char_mat(5,5)=( 0.d0, 1.d0)
char_mat(5,6)=( 0.d0,-1.d0)
char_mat(5,7)=CMPLX( dsq2,-dsq2)
char_mat(5,8)=CMPLX(-dsq2, dsq2)
char_mat(5,9)=(-1.d0, 0.d0)
char_mat(5,11)=CMPLX(-dsq2,-dsq2)
char_mat(5,12)=CMPLX( dsq2, dsq2)
char_mat(5,13)=( 0.d0,-1.d0)
char_mat(5,14)=( 0.d0, 1.d0)
char_mat(5,15)=CMPLX(-dsq2, dsq2)
char_mat(5,16)=CMPLX( dsq2,-dsq2)
name_rap(6)="G_6- "
char_mat(6,3)=CMPLX( dsq2,-dsq2)
char_mat(6,4)=CMPLX(-dsq2, dsq2)
char_mat(6,5)=( 0.d0,-1.d0)
char_mat(6,6)=( 0.d0, 1.d0)
char_mat(6,7)=CMPLX( dsq2, dsq2)
char_mat(6,8)=CMPLX(-dsq2,-dsq2)
char_mat(6,9)=(-1.d0, 0.d0)
char_mat(6,11)=CMPLX(-dsq2, dsq2)
char_mat(6,12)=CMPLX( dsq2,-dsq2)
char_mat(6,13)=( 0.d0, 1.d0)
char_mat(6,14)=( 0.d0,-1.d0)
char_mat(6,15)=CMPLX(-dsq2,-dsq2)
char_mat(6,16)=CMPLX( dsq2, dsq2)
name_rap(7)="G_7- "
char_mat(7,3)=CMPLX(-dsq2,-dsq2)
char_mat(7,4)=CMPLX( dsq2, dsq2)
char_mat(7,5)=( 0.d0, 1.d0)
char_mat(7,6)=( 0.d0,-1.d0)
char_mat(7,7)=CMPLX(-dsq2, dsq2)
char_mat(7,8)=CMPLX( dsq2,-dsq2)
char_mat(7,9)=(-1.d0, 0.d0)
char_mat(7,11)=CMPLX( dsq2, dsq2)
char_mat(7,12)=CMPLX(-dsq2,-dsq2)
char_mat(7,13)=( 0.d0,-1.d0)
char_mat(7,14)=( 0.d0, 1.d0)
char_mat(7,15)=CMPLX( dsq2,-dsq2)
char_mat(7,16)=CMPLX(-dsq2, dsq2)
name_rap(8)="G_8- "
char_mat(8,3)=CMPLX(-dsq2, dsq2)
char_mat(8,4)=CMPLX( dsq2,-dsq2)
char_mat(8,5)=( 0.d0,-1.d0)
char_mat(8,6)=( 0.d0, 1.d0)
char_mat(8,7)=CMPLX(-dsq2,-dsq2)
char_mat(8,8)=CMPLX( dsq2, dsq2)
char_mat(8,9)=(-1.d0, 0.d0)
char_mat(8,11)=CMPLX( dsq2,-dsq2)
char_mat(8,12)=CMPLX(-dsq2, dsq2)
char_mat(8,13)=( 0.d0, 1.d0)
char_mat(8,14)=( 0.d0,-1.d0)
char_mat(8,15)=CMPLX( dsq2, dsq2)
char_mat(8,16)=CMPLX(-dsq2,-dsq2)
ELSEIF (code_group==19) THEN
!
! C_6h NB: The signs of the characters of C3^2 -C3^2 C6^5 -C6^5 S6 -S6 S3 -S3
! are changed with respect to Koster, Space groups and their
! representation. They match the table in Koster, Dimmok,
! Wheeler, Statz, Properties of the 32 point groups.
!
nclass_ref=24
name_class(3)="C6 "
name_class(4)="-C6 "
name_class(5)="C3 "
name_class(6)="-C3 "
name_class(7)="C2 "
name_class(8)="-C2 "
name_class(9)="C3^2"
name_class(10)="-C3^2"
name_class(11)="C6^5"
name_class(12)="-C6^5"
name_class(13)="i "
name_class(14)="-i "
name_class(15)="S3^5"
name_class(16)="-S3^5"
name_class(17)="S6^5"
name_class(18)="-S6^5"
name_class(19)="s_h "
name_class(20)="-s_h"
name_class(21)="S6 "
name_class(22)="-S6 "
name_class(23)="S3 "
name_class(24)="-S3 "
nrap_ref=12
name_rap(1)="G_7+ "
char_mat(1,3)=CMPLX( sqr3d2, 0.5d0)
char_mat(1,4)=CMPLX(-sqr3d2,-0.5d0)
char_mat(1,5)=CMPLX( 0.5d0, sqr3d2)
char_mat(1,6)=CMPLX(-0.5d0,-sqr3d2)
char_mat(1,7)=( 0.d0, 1.0d0)
char_mat(1,8)=( 0.d0,-1.0d0)
! char_mat(1,9)=CMPLX(-0.5d0, sqr3d2)
! char_mat(1,10)=CMPLX( 0.5d0,-sqr3d2)
! char_mat(1,11)=CMPLX(-sqr3d2, 0.5d0)
! char_mat(1,12)=CMPLX( sqr3d2,-0.5d0)
char_mat(1,9)=CMPLX( 0.5d0,-sqr3d2)
char_mat(1,10)=CMPLX(-0.5d0, sqr3d2)
char_mat(1,11)=CMPLX( sqr3d2,-0.5d0)
char_mat(1,12)=CMPLX(-sqr3d2, 0.5d0)
char_mat(1,14)=(-1.0d0, 0.d0)
char_mat(1,15)=CMPLX( sqr3d2, 0.5d0)
char_mat(1,16)=CMPLX(-sqr3d2,-0.5d0)
char_mat(1,17)=CMPLX( 0.5d0, sqr3d2)
char_mat(1,18)=CMPLX(-0.5d0,-sqr3d2)
char_mat(1,19)=( 0.d0, 1.0d0)
char_mat(1,20)=( 0.d0,-1.0d0)
! char_mat(1,21)=CMPLX(-0.5d0, sqr3d2)
! char_mat(1,22)=CMPLX( 0.5d0,-sqr3d2)
! char_mat(1,23)=CMPLX(-sqr3d2, 0.5d0)
! char_mat(1,24)=CMPLX( sqr3d2,-0.5d0)
char_mat(1,21)=CMPLX( 0.5d0,-sqr3d2)
char_mat(1,22)=CMPLX(-0.5d0, sqr3d2)
char_mat(1,23)=CMPLX( sqr3d2,-0.5d0)
char_mat(1,24)=CMPLX(-sqr3d2, 0.5d0)
name_rap(2)="G_8+ "
char_mat(2,3)=CMPLX( sqr3d2,-0.5d0)
char_mat(2,4)=CMPLX(-sqr3d2, 0.5d0)
char_mat(2,5)=CMPLX( 0.5d0,-sqr3d2)
char_mat(2,6)=CMPLX(-0.5d0, sqr3d2)
char_mat(2,7)=( 0.d0,-1.0d0)
char_mat(2,8)=( 0.d0, 1.0d0)
! char_mat(2,9)=CMPLX(-0.5d0,-sqr3d2)
! char_mat(2,10)=CMPLX( 0.5d0, sqr3d2)
! char_mat(2,11)=CMPLX(-sqr3d2,-0.5d0)
! char_mat(2,12)=CMPLX( sqr3d2, 0.5d0)
char_mat(2,9)=CMPLX( 0.5d0, sqr3d2)
char_mat(2,10)=CMPLX(-0.5d0,-sqr3d2)
char_mat(2,11)=CMPLX( sqr3d2, 0.5d0)
char_mat(2,12)=CMPLX(-sqr3d2,-0.5d0)
char_mat(2,14)=(-1.0d0, 0.d0)
char_mat(2,15)=CMPLX( sqr3d2,-0.5d0)
char_mat(2,16)=CMPLX(-sqr3d2, 0.5d0)
char_mat(2,17)=CMPLX( 0.5d0,-sqr3d2)
char_mat(2,18)=CMPLX(-0.5d0, sqr3d2)
char_mat(2,19)=( 0.d0,-1.0d0)
char_mat(2,20)=( 0.d0, 1.0d0)
! char_mat(2,21)=CMPLX(-0.5d0,-sqr3d2)
! char_mat(2,22)=CMPLX( 0.5d0, sqr3d2)
! char_mat(2,23)=CMPLX(-sqr3d2,-0.5d0)
! char_mat(2,24)=CMPLX( sqr3d2, 0.5d0)
char_mat(2,21)=CMPLX( 0.5d0, sqr3d2)
char_mat(2,22)=CMPLX(-0.5d0,-sqr3d2)
char_mat(2,23)=CMPLX( sqr3d2, 0.5d0)
char_mat(2,24)=CMPLX(-sqr3d2,-0.5d0)
name_rap(3)="G_11+ "
char_mat(3,3)=( 0.d0, 1.0d0)
char_mat(3,4)=( 0.d0,-1.0d0)
char_mat(3,5)=(-1.d0, 0.d0 )
char_mat(3,7)=( 0.d0,-1.0d0)
char_mat(3,8)=( 0.d0, 1.0d0)
! char_mat(3,10)=(-1.d0, 0.d0 )
! char_mat(3,11)=( 0.d0, 1.0d0)
! char_mat(3,12)=( 0.d0,-1.0d0)
char_mat(3,9)=(-1.d0, 0.d0 )
char_mat(3,11)=( 0.d0,-1.0d0)
char_mat(3,12)=( 0.d0, 1.0d0)
char_mat(3,14)=(-1.0d0, 0.d0)
char_mat(3,15)=( 0.d0, 1.0d0)
char_mat(3,16)=( 0.d0,-1.0d0)
char_mat(3,17)=(-1.0d0, 0.d0)
char_mat(3,19)=( 0.d0,-1.0d0)
char_mat(3,20)=( 0.d0, 1.0d0)
! char_mat(3,22)=(-1.0d0, 0.d0)
! char_mat(3,23)=( 0.d0, 1.0d0)
! char_mat(3,24)=( 0.d0,-1.0d0)
char_mat(3,21)=(-1.0d0, 0.d0)
char_mat(3,23)=( 0.d0,-1.0d0)
char_mat(3,24)=( 0.d0, 1.0d0)
name_rap(4)="G_12+ "
char_mat(4,3)=( 0.d0,-1.0d0)
char_mat(4,4)=( 0.d0, 1.0d0)
char_mat(4,5)=(-1.d0, 0.d0 )
char_mat(4,7)=( 0.d0, 1.0d0)
char_mat(4,8)=( 0.d0,-1.0d0)
! char_mat(4,10)=(-1.d0, 0.d0 )
! char_mat(4,11)=( 0.d0,-1.0d0)
! char_mat(4,12)=( 0.d0, 1.0d0)
char_mat(4,9)=(-1.d0, 0.d0 )
char_mat(4,11)=( 0.d0, 1.0d0)
char_mat(4,12)=( 0.d0,-1.0d0)
char_mat(4,14)=(-1.0d0, 0.d0)
char_mat(4,15)=( 0.d0,-1.0d0)
char_mat(4,16)=( 0.d0, 1.0d0)
char_mat(4,17)=(-1.0d0, 0.d0)
char_mat(4,19)=( 0.d0, 1.0d0)
char_mat(4,20)=( 0.d0,-1.0d0)
! char_mat(4,22)=(-1.0d0, 0.d0)
! char_mat(4,23)=( 0.d0,-1.0d0)
! char_mat(4,24)=( 0.d0, 1.0d0)
char_mat(4,21)=(-1.0d0, 0.d0)
char_mat(4,23)=( 0.d0, 1.0d0)
char_mat(4,24)=( 0.d0,-1.0d0)
name_rap(5)="G_9+ "
char_mat(5,3)=CMPLX(-sqr3d2,-0.5d0)
char_mat(5,4)=CMPLX( sqr3d2, 0.5d0)
char_mat(5,5)=CMPLX( 0.5d0, sqr3d2)
char_mat(5,6)=CMPLX(-0.5d0,-sqr3d2)
char_mat(5,7)=( 0.d0,-1.0d0)
char_mat(5,8)=( 0.d0, 1.0d0)
! char_mat(5,9)=CMPLX(-0.5d0, sqr3d2)
! char_mat(5,10)=CMPLX( 0.5d0,-sqr3d2)
! char_mat(5,11)=CMPLX( sqr3d2,-0.5d0)
! char_mat(5,12)=CMPLX(-sqr3d2, 0.5d0)
char_mat(5,9)=CMPLX( 0.5d0,-sqr3d2)
char_mat(5,10)=CMPLX(-0.5d0, sqr3d2)
char_mat(5,11)=CMPLX(-sqr3d2, 0.5d0)
char_mat(5,12)=CMPLX( sqr3d2,-0.5d0)
char_mat(5,14)=(-1.0d0, 0.d0)
char_mat(5,15)=CMPLX(-sqr3d2,-0.5d0)
char_mat(5,16)=CMPLX( sqr3d2, 0.5d0)
char_mat(5,17)=CMPLX( 0.5d0, sqr3d2)
char_mat(5,18)=CMPLX(-0.5d0,-sqr3d2)
char_mat(5,19)=( 0.d0,-1.0d0)
char_mat(5,20)=( 0.d0, 1.0d0)
! char_mat(5,21)=CMPLX(-0.5d0, sqr3d2)
! char_mat(5,22)=CMPLX( 0.5d0,-sqr3d2)
! char_mat(5,23)=CMPLX( sqr3d2,-0.5d0)
! char_mat(5,24)=CMPLX(-sqr3d2, 0.5d0)
char_mat(5,21)=CMPLX( 0.5d0,-sqr3d2)
char_mat(5,22)=CMPLX(-0.5d0, sqr3d2)
char_mat(5,23)=CMPLX(-sqr3d2, 0.5d0)
char_mat(5,24)=CMPLX( sqr3d2,-0.5d0)
name_rap(6)="G_10+ "
char_mat(6,3)=CMPLX(-sqr3d2, 0.5d0)
char_mat(6,4)=CMPLX( sqr3d2,-0.5d0)
char_mat(6,5)=CMPLX( 0.5d0,-sqr3d2)
char_mat(6,6)=CMPLX(-0.5d0, sqr3d2)
char_mat(6,7)=( 0.d0, 1.0d0)
char_mat(6,8)=( 0.d0,-1.0d0)
! char_mat(6,9)=CMPLX(-0.5d0,-sqr3d2)
! char_mat(6,10)=CMPLX( 0.5d0, sqr3d2)
! char_mat(6,11)=CMPLX( sqr3d2, 0.5d0)
! char_mat(6,12)=CMPLX(-sqr3d2,-0.5d0)
char_mat(6,9)=CMPLX( 0.5d0, sqr3d2)
char_mat(6,10)=CMPLX(-0.5d0,-sqr3d2)
char_mat(6,11)=CMPLX(-sqr3d2,-0.5d0)
char_mat(6,12)=CMPLX( sqr3d2, 0.5d0)
char_mat(6,14)=(-1.0d0, 0.d0)
char_mat(6,15)=CMPLX(-sqr3d2, 0.5d0)
char_mat(6,16)=CMPLX( sqr3d2,-0.5d0)
char_mat(6,17)=CMPLX( 0.5d0,-sqr3d2)
char_mat(6,18)=CMPLX(-0.5d0, sqr3d2)
char_mat(6,19)=( 0.d0, 1.0d0)
char_mat(6,20)=( 0.d0,-1.0d0)
! char_mat(6,21)=CMPLX(-0.5d0,-sqr3d2)
! char_mat(6,22)=CMPLX( 0.5d0, sqr3d2)
! char_mat(6,23)=CMPLX( sqr3d2, 0.5d0)
! char_mat(6,24)=CMPLX(-sqr3d2,-0.5d0)
char_mat(6,21)=CMPLX( 0.5d0, sqr3d2)
char_mat(6,22)=CMPLX(-0.5d0,-sqr3d2)
char_mat(6,23)=CMPLX(-sqr3d2,-0.5d0)
char_mat(6,24)=CMPLX( sqr3d2, 0.5d0)
name_rap(7)="G_7- "
char_mat(7,3)=CMPLX( sqr3d2, 0.5d0)
char_mat(7,4)=CMPLX(-sqr3d2,-0.5d0)
char_mat(7,5)=CMPLX( 0.5d0, sqr3d2)
char_mat(7,6)=CMPLX(-0.5d0,-sqr3d2)
char_mat(7,7)=( 0.d0, 1.0d0)
char_mat(7,8)=( 0.d0,-1.0d0)
! char_mat(7,9)=CMPLX(-0.5d0, sqr3d2)
! char_mat(7,10)=CMPLX( 0.5d0,-sqr3d2)
! char_mat(7,11)=CMPLX(-sqr3d2, 0.5d0)
! char_mat(7,12)=CMPLX( sqr3d2,-0.5d0)
char_mat(7,9)=CMPLX( 0.5d0,-sqr3d2)
char_mat(7,10)=CMPLX(-0.5d0, sqr3d2)
char_mat(7,11)=CMPLX( sqr3d2,-0.5d0)
char_mat(7,12)=CMPLX(-sqr3d2, 0.5d0)
char_mat(7,13)=(-1.0d0, 0.d0)
char_mat(7,15)=CMPLX(-sqr3d2,-0.5d0)
char_mat(7,16)=CMPLX( sqr3d2, 0.5d0)
char_mat(7,17)=CMPLX(-0.5d0,-sqr3d2)
char_mat(7,18)=CMPLX( 0.5d0, sqr3d2)
char_mat(7,19)=( 0.d0,-1.0d0)
char_mat(7,20)=( 0.d0, 1.0d0)
! char_mat(7,21)=CMPLX( 0.5d0,-sqr3d2)
! char_mat(7,22)=CMPLX(-0.5d0, sqr3d2)
! char_mat(7,23)=CMPLX( sqr3d2,-0.5d0)
! char_mat(7,24)=CMPLX(-sqr3d2, 0.5d0)
char_mat(7,21)=CMPLX(-0.5d0, sqr3d2)
char_mat(7,22)=CMPLX( 0.5d0,-sqr3d2)
char_mat(7,23)=CMPLX(-sqr3d2, 0.5d0)
char_mat(7,24)=CMPLX( sqr3d2,-0.5d0)
name_rap(8)="G_8- "
char_mat(8,3)=CMPLX( sqr3d2,-0.5d0)
char_mat(8,4)=CMPLX(-sqr3d2, 0.5d0)
char_mat(8,5)=CMPLX( 0.5d0,-sqr3d2)
char_mat(8,6)=CMPLX(-0.5d0, sqr3d2)
char_mat(8,7)=( 0.d0,-1.0d0)
char_mat(8,8)=( 0.d0, 1.0d0)
! char_mat(8,9)=CMPLX(-0.5d0,-sqr3d2)
! char_mat(8,10)=CMPLX( 0.5d0, sqr3d2)
! char_mat(8,11)=CMPLX(-sqr3d2,-0.5d0)
! char_mat(8,12)=CMPLX( sqr3d2, 0.5d0)
char_mat(8,9)=CMPLX( 0.5d0, sqr3d2)
char_mat(8,10)=CMPLX(-0.5d0,-sqr3d2)
char_mat(8,11)=CMPLX( sqr3d2, 0.5d0)
char_mat(8,12)=CMPLX(-sqr3d2,-0.5d0)
char_mat(8,13)=(-1.0d0, 0.d0)
char_mat(8,15)=CMPLX(-sqr3d2, 0.5d0)
char_mat(8,16)=CMPLX( sqr3d2,-0.5d0)
char_mat(8,17)=CMPLX(-0.5d0, sqr3d2)
char_mat(8,18)=CMPLX( 0.5d0,-sqr3d2)
char_mat(8,19)=( 0.d0, 1.0d0)
char_mat(8,20)=( 0.d0,-1.0d0)
! char_mat(8,21)=CMPLX( 0.5d0, sqr3d2)
! char_mat(8,22)=CMPLX(-0.5d0,-sqr3d2)
! char_mat(8,23)=CMPLX( sqr3d2, 0.5d0)
! char_mat(8,24)=CMPLX(-sqr3d2,-0.5d0)
char_mat(8,21)=CMPLX(-0.5d0,-sqr3d2)
char_mat(8,22)=CMPLX( 0.5d0, sqr3d2)
char_mat(8,23)=CMPLX(-sqr3d2,-0.5d0)
char_mat(8,24)=CMPLX( sqr3d2, 0.5d0)
name_rap(9)="G_11-"
char_mat(9,3)=( 0.d0, 1.0d0)
char_mat(9,4)=( 0.d0,-1.0d0)
char_mat(9,5)=(-1.d0, 0.d0 )
char_mat(9,7)=( 0.d0,-1.0d0)
char_mat(9,8)=( 0.d0, 1.0d0)
! char_mat(9,10)=(-1.d0, 0.d0 )
! char_mat(9,11)=( 0.d0, 1.0d0)
! char_mat(9,12)=( 0.d0,-1.0d0)
char_mat(9,9)=(-1.d0, 0.d0 )
char_mat(9,11)=( 0.d0,-1.0d0)
char_mat(9,12)=( 0.d0, 1.0d0)
char_mat(9,13)=(-1.0d0, 0.d0)
char_mat(9,15)=( 0.d0,-1.0d0)
char_mat(9,16)=( 0.d0, 1.0d0)
char_mat(9,18)=(-1.0d0, 0.d0)
char_mat(9,19)=( 0.d0, 1.0d0)
char_mat(9,20)=( 0.d0,-1.0d0)
! char_mat(9,21)=(-1.0d0, 0.d0)
! char_mat(9,23)=( 0.d0,-1.0d0)
! char_mat(9,24)=( 0.d0, 1.0d0)
char_mat(9,22)=(-1.0d0, 0.d0)
char_mat(9,23)=( 0.d0, 1.0d0)
char_mat(9,24)=( 0.d0,-1.0d0)
name_rap(10)="G_12-"
char_mat(10,3) =( 0.d0,-1.0d0)
char_mat(10,4) =( 0.d0, 1.0d0)
char_mat(10,5) =(-1.d0, 0.d0 )
char_mat(10,7) =( 0.d0, 1.0d0)
char_mat(10,8) =( 0.d0,-1.0d0)
! char_mat(10,10)=(-1.d0, 0.d0 )
! char_mat(10,11)=( 0.d0,-1.0d0)
! char_mat(10,12)=( 0.d0, 1.0d0)
char_mat(10,9)=(-1.d0, 0.d0 )
char_mat(10,11)=( 0.d0, 1.0d0)
char_mat(10,12)=( 0.d0,-1.0d0)
char_mat(10,13)=(-1.0d0, 0.d0)
char_mat(10,15)=( 0.d0, 1.0d0)
char_mat(10,16)=( 0.d0,-1.0d0)
char_mat(10,18)=(-1.0d0, 0.d0)
char_mat(10,19)=( 0.d0,-1.0d0)
char_mat(10,20)=( 0.d0, 1.0d0)
! char_mat(10,21)=(-1.0d0, 0.d0)
! char_mat(10,23)=( 0.d0, 1.0d0)
! char_mat(10,24)=( 0.d0,-1.0d0)
char_mat(10,22)=(-1.0d0, 0.d0)
char_mat(10,23)=( 0.d0,-1.0d0)
char_mat(10,24)=( 0.d0, 1.0d0)
name_rap(11)="G_9- "
char_mat(11,3)=CMPLX(-sqr3d2,-0.5d0)
char_mat(11,4)=CMPLX( sqr3d2, 0.5d0)
char_mat(11,5)=CMPLX( 0.5d0, sqr3d2)
char_mat(11,6)=CMPLX(-0.5d0,-sqr3d2)
char_mat(11,7)=( 0.d0,-1.0d0)
char_mat(11,8)=( 0.d0, 1.0d0)
! char_mat(11,9)=CMPLX(-0.5d0, sqr3d2)
! char_mat(11,10)=CMPLX( 0.5d0,-sqr3d2)
! char_mat(11,11)=CMPLX( sqr3d2,-0.5d0)
! char_mat(11,12)=CMPLX(-sqr3d2, 0.5d0)
char_mat(11,9)=CMPLX( 0.5d0,-sqr3d2)
char_mat(11,10)=CMPLX(-0.5d0, sqr3d2)
char_mat(11,11)=CMPLX(-sqr3d2, 0.5d0)
char_mat(11,12)=CMPLX( sqr3d2,-0.5d0)
char_mat(11,13)=(-1.0d0, 0.d0)
char_mat(11,15)=CMPLX( sqr3d2, 0.5d0)
char_mat(11,16)=CMPLX(-sqr3d2,-0.5d0)
char_mat(11,17)=CMPLX(-0.5d0,-sqr3d2)
char_mat(11,18)=CMPLX( 0.5d0, sqr3d2)
char_mat(11,19)=( 0.d0, 1.0d0)
char_mat(11,20)=( 0.d0,-1.0d0)
! char_mat(11,21)=CMPLX( 0.5d0,-sqr3d2)
! char_mat(11,22)=CMPLX(-0.5d0, sqr3d2)
! char_mat(11,23)=CMPLX(-sqr3d2, 0.5d0)
! char_mat(11,24)=CMPLX( sqr3d2,-0.5d0)
char_mat(11,21)=CMPLX(-0.5d0, sqr3d2)
char_mat(11,22)=CMPLX( 0.5d0,-sqr3d2)
char_mat(11,23)=CMPLX( sqr3d2,-0.5d0)
char_mat(11,24)=CMPLX(-sqr3d2, 0.5d0)
name_rap(12)="G_10- "
char_mat(12,3)=CMPLX(-sqr3d2, 0.5d0)
char_mat(12,4)=CMPLX( sqr3d2,-0.5d0)
char_mat(12,5)=CMPLX( 0.5d0,-sqr3d2)
char_mat(12,6)=CMPLX(-0.5d0, sqr3d2)
char_mat(12,7)=( 0.d0, 1.0d0)
char_mat(12,8)=( 0.d0,-1.0d0)
! char_mat(12,9)=CMPLX(-0.5d0,-sqr3d2)
! char_mat(12,10)=CMPLX( 0.5d0, sqr3d2)
! char_mat(12,11)=CMPLX( sqr3d2, 0.5d0)
! char_mat(12,12)=CMPLX(-sqr3d2,-0.5d0)
char_mat(12,9)=CMPLX( 0.5d0, sqr3d2)
char_mat(12,10)=CMPLX(-0.5d0,-sqr3d2)
char_mat(12,11)=CMPLX(-sqr3d2,-0.5d0)
char_mat(12,12)=CMPLX( sqr3d2, 0.5d0)
char_mat(12,13)=(-1.0d0, 0.d0)
char_mat(12,15)=CMPLX( sqr3d2,-0.5d0)
char_mat(12,16)=CMPLX(-sqr3d2, 0.5d0)
char_mat(12,17)=CMPLX(-0.5d0, sqr3d2)
char_mat(12,18)=CMPLX( 0.5d0,-sqr3d2)
char_mat(12,19)=( 0.d0,-1.0d0)
char_mat(12,20)=( 0.d0, 1.0d0)
! char_mat(12,21)=CMPLX( 0.5d0, sqr3d2)
! char_mat(12,22)=CMPLX(-0.5d0,-sqr3d2)
! char_mat(12,23)=CMPLX(-sqr3d2,-0.5d0)
! char_mat(12,24)=CMPLX( sqr3d2, 0.5d0)
char_mat(12,21)=CMPLX(-0.5d0,-sqr3d2)
char_mat(12,22)=CMPLX( 0.5d0, sqr3d2)
char_mat(12,23)=CMPLX( sqr3d2, 0.5d0)
char_mat(12,24)=CMPLX(-sqr3d2,-0.5d0)
ELSEIF (code_group==20) THEN
!
! D_2h
!
nclass_ref=10
name_class(3)=" C2 "
name_class1(3)="-C2 "
name_class(4)=" C2' "
name_class1(4)="-C2'"
name_class(5)="C2'' "
name_class1(5)="-C2''"
name_class(6)="i "
name_class(7)="-i "
name_class(8)=" s_v"
name_class1(8)="-s_v"
name_class(9)=" s_v'"
name_class1(9)="-s_v'"
name_class(10)="s_v''"
name_class1(10)="-s_v''"
nrap_ref=2
name_rap(1)="G_5+ "
char_mat(1,1)=( 2.d0, 0.d0)
char_mat(1,2)=(-2.d0, 0.d0)
char_mat(1,3)=( 0.d0, 0.d0)
char_mat(1,4)=( 0.d0, 0.d0)
char_mat(1,5)=( 0.d0, 0.d0)
char_mat(1,6)=( 2.d0, 0.d0)
char_mat(1,7)=(-2.d0, 0.d0)
char_mat(1,8)=( 0.d0, 0.d0)
char_mat(1,9)=( 0.d0, 0.d0)
char_mat(1,10)=( 0.d0, 0.d0)
name_rap(2)="G_5- "
char_mat(2,1)=( 2.d0, 0.d0)
char_mat(2,2)=(-2.d0, 0.d0)
char_mat(2,3)=( 0.d0, 0.d0)
char_mat(2,4)=( 0.d0, 0.d0)
char_mat(2,5)=( 0.d0, 0.d0)
char_mat(2,6)=(-2.d0, 0.d0)
char_mat(2,7)=( 2.d0, 0.d0)
char_mat(2,8)=( 0.d0, 0.d0)
char_mat(2,9)=( 0.d0, 0.d0)
char_mat(2,10)=( 0.d0, 0.d0)
ELSEIF (code_group==21) THEN
!
! D_3h
!
nclass_ref=9
name_class(3)="2C3 "
name_class(4)="-2C3"
name_class(5)=" 3C2'"
name_class1(5)="-3C2'"
name_class(6)=" s_h"
name_class1(6)="-s_h'"
name_class(7)="2S3 "
name_class(8)="-2S3"
name_class(9)=" 3s_v"
name_class1(9)="-3s_v"
nrap_ref=3
name_rap(1)="G_7 "
char_mat(1,1)=( 2.d0, 0.d0)
char_mat(1,2)=(-2.d0, 0.d0)
char_mat(1,4)=(-1.d0, 0.d0)
char_mat(1,5)=( 0.d0, 0.d0)
char_mat(1,6)=( 0.d0, 0.d0)
char_mat(1,7)=CMPLX( sqrt3, 0.d0)
char_mat(1,8)=CMPLX(-sqrt3, 0.d0)
char_mat(1,9)=( 0.d0, 0.d0)
name_rap(2)="G_8 "
char_mat(2,1)=( 2.d0, 0.d0)
char_mat(2,2)=(-2.d0, 0.d0)
char_mat(2,4)=(-1.d0, 0.d0)
char_mat(2,5)=( 0.d0, 0.d0)
char_mat(2,6)=( 0.d0, 0.d0)
char_mat(2,7)=CMPLX(-sqrt3, 0.d0)
char_mat(2,8)=CMPLX( sqrt3, 0.d0)
char_mat(2,9)=( 0.d0, 0.d0)
name_rap(3)="G_9 "
char_mat(3,1)=( 2.d0, 0.d0)
char_mat(3,2)=(-2.d0, 0.d0)
char_mat(3,3)=(-2.d0, 0.d0)
char_mat(3,4)=( 2.d0, 0.d0)
char_mat(3,5)=( 0.d0, 0.d0)
char_mat(3,6)=( 0.d0, 0.d0)
char_mat(3,7)=( 0.d0, 0.d0)
char_mat(3,8)=( 0.d0, 0.d0)
char_mat(3,9)=( 0.d0, 0.d0)
ELSEIF (code_group==22) THEN
!
! D_4h
!
nclass_ref=14
name_class(3)="2C4 "
name_class(4)="-2C4"
name_class(5)=" C2 "
name_class1(5)="-C2 "
name_class(6)=" 2C2'"
name_class1(6)="-2C2' "
name_class(7)="2C2''"
name_class1(7)="-2C2''"
name_class(8)="i "
name_class(9)="-i "
name_class(10)="2S4 "
name_class(11)="-2S4"
name_class(12)=" s_h"
name_class1(12)="-s_h"
name_class(13)=" 2s_v"
name_class1(13)="-2s_v"
name_class(14)=" 2s_d"
name_class1(14)="-2s_d"
nrap_ref=4
name_rap(1)="G_6+ M_6+"
char_mat(1,1)=( 2.d0, 0.d0)
char_mat(1,2)=(-2.d0, 0.d0)
char_mat(1,3)=CMPLX( sqrt2, 0.d0)
char_mat(1,4)=CMPLX(-sqrt2, 0.d0)
char_mat(1,5)=( 0.d0, 0.d0)
char_mat(1,6)=( 0.d0, 0.d0)
char_mat(1,7)=( 0.d0, 0.d0)
char_mat(1,8)=( 2.d0, 0.d0)
char_mat(1,9)=(-2.d0, 0.d0)
char_mat(1,10)=CMPLX( sqrt2, 0.d0)
char_mat(1,11)=CMPLX(-sqrt2, 0.d0)
char_mat(1,12)=( 0.d0, 0.d0)
char_mat(1,13)=( 0.d0, 0.d0)
char_mat(1,14)=( 0.d0, 0.d0)
name_rap(2)="G_7+ M_7+"
char_mat(2,1)=( 2.d0, 0.d0)
char_mat(2,2)=(-2.d0, 0.d0)
char_mat(2,3)=CMPLX(-sqrt2, 0.d0)
char_mat(2,4)=CMPLX( sqrt2, 0.d0)
char_mat(2,5)=( 0.d0, 0.d0)
char_mat(2,6)=( 0.d0, 0.d0)
char_mat(2,7)=( 0.d0, 0.d0)
char_mat(2,8)=( 2.d0, 0.d0)
char_mat(2,9)=(-2.d0, 0.d0)
char_mat(2,10)=CMPLX(-sqrt2, 0.d0)
char_mat(2,11)=CMPLX( sqrt2, 0.d0)
char_mat(2,12)=( 0.d0, 0.d0)
char_mat(2,13)=( 0.d0, 0.d0)
char_mat(2,14)=( 0.d0, 0.d0)
name_rap(3)="G_6- M_6- "
char_mat(3,1)=( 2.d0, 0.d0)
char_mat(3,2)=(-2.d0, 0.d0)
char_mat(3,3)=CMPLX( sqrt2, 0.d0)
char_mat(3,4)=CMPLX(-sqrt2, 0.d0)
char_mat(3,5)=( 0.d0, 0.d0)
char_mat(3,6)=( 0.d0, 0.d0)
char_mat(3,7)=( 0.d0, 0.d0)
char_mat(3,8)=(-2.d0, 0.d0)
char_mat(3,9)=( 2.d0, 0.d0)
char_mat(3,10)=CMPLX(-sqrt2, 0.d0)
char_mat(3,11)=CMPLX( sqrt2, 0.d0)
char_mat(3,12)=( 0.d0, 0.d0)
char_mat(3,13)=( 0.d0, 0.d0)
char_mat(3,14)=( 0.d0, 0.d0)
name_rap(4)="G_7- M_7- "
char_mat(4,1)=( 2.d0, 0.d0)
char_mat(4,2)=(-2.d0, 0.d0)
char_mat(4,3)=CMPLX(-sqrt2, 0.d0)
char_mat(4,4)=CMPLX( sqrt2, 0.d0)
char_mat(4,5)=( 0.d0, 0.d0)
char_mat(4,6)=( 0.d0, 0.d0)
char_mat(4,7)=( 0.d0, 0.d0)
char_mat(4,8)=(-2.d0, 0.d0)
char_mat(4,9)=( 2.d0, 0.d0)
char_mat(4,10)=CMPLX( sqrt2, 0.d0)
char_mat(4,11)=CMPLX(-sqrt2, 0.d0)
char_mat(4,12)=( 0.d0, 0.d0)
char_mat(4,13)=( 0.d0, 0.d0)
char_mat(4,14)=( 0.d0, 0.d0)
ELSEIF (code_group==23) THEN
!
! D_6h
!
nclass_ref=18
name_class(3)="C2 "
name_class1(3)="-C2 "
name_class(4)="2C3 "
name_class(5)="-2C3 "
name_class(6)="2C6 "
name_class(7)="-2C6 "
name_class(8)=" 3C2'"
name_class1(8)="-3C2'"
name_class(9)="3C2''"
name_class1(9)="-3C2''"
name_class(10)=" i "
name_class(11)="-i "
name_class(12)=" s_h"
name_class1(12)="-s_h"
name_class(13)="2S6"
name_class(14)="-2S6"
name_class(15)="2S3"
name_class(16)="-2S3"
name_class(17)=" 3s_v"
name_class1(17)="-3s_v"
name_class(18)=" 3s_d"
name_class1(18)="-3s_d"
nrap_ref=6
name_rap(1)="G_7+ "
char_mat(1,1)=( 2.d0, 0.d0)
char_mat(1,2)=(-2.d0, 0.d0)
char_mat(1,3)=( 0.d0, 0.d0)
char_mat(1,4)=( 1.d0, 0.d0)
char_mat(1,5)=(-1.d0, 0.d0)
char_mat(1,6)=CMPLX( sqrt3, 0.d0)
char_mat(1,7)=CMPLX(-sqrt3, 0.d0)
char_mat(1,8)=( 0.d0, 0.d0)
char_mat(1,9)=( 0.d0, 0.d0)
char_mat(1,10)=( 2.d0, 0.d0)
char_mat(1,11)=(-2.d0, 0.d0)
char_mat(1,12)=( 0.d0, 0.d0)
char_mat(1,13)=( 1.d0, 0.d0)
char_mat(1,14)=(-1.d0, 0.d0)
char_mat(1,15)=CMPLX( sqrt3, 0.d0)
char_mat(1,16)=CMPLX(-sqrt3, 0.d0)
char_mat(1,17)=( 0.d0, 0.d0)
char_mat(1,18)=( 0.d0, 0.d0)
name_rap(2)="G_8+ "
char_mat(2,1)=( 2.d0, 0.d0)
char_mat(2,2)=(-2.d0, 0.d0)
char_mat(2,3)=( 0.d0, 0.d0)
char_mat(2,4)=( 1.d0, 0.d0)
char_mat(2,5)=(-1.d0, 0.d0)
char_mat(2,6)=CMPLX(-sqrt3, 0.d0)
char_mat(2,7)=CMPLX( sqrt3, 0.d0)
char_mat(2,8)=( 0.d0, 0.d0)
char_mat(2,9)=( 0.d0, 0.d0)
char_mat(2,10)=( 2.d0, 0.d0)
char_mat(2,11)=(-2.d0, 0.d0)
char_mat(2,12)=( 0.d0, 0.d0)
char_mat(2,13)=( 1.d0, 0.d0)
char_mat(2,14)=(-1.d0, 0.d0)
char_mat(2,15)=CMPLX(-sqrt3, 0.d0)
char_mat(2,16)=CMPLX( sqrt3, 0.d0)
char_mat(2,17)=( 0.d0, 0.d0)
char_mat(2,18)=( 0.d0, 0.d0)
name_rap(3)="G_9+ "
char_mat(3,1)=( 2.d0, 0.d0)
char_mat(3,2)=(-2.d0, 0.d0)
char_mat(3,3)=( 0.d0, 0.d0)
char_mat(3,4)=(-2.d0, 0.d0)
char_mat(3,5)=( 2.d0, 0.d0)
char_mat(3,6)=( 0.d0, 0.d0)
char_mat(3,7)=( 0.d0, 0.d0)
char_mat(3,8)=( 0.d0, 0.d0)
char_mat(3,9)=( 0.d0, 0.d0)
char_mat(3,10)=( 2.d0, 0.d0)
char_mat(3,11)=(-2.d0, 0.d0)
char_mat(3,12)=( 0.d0, 0.d0)
char_mat(3,13)=(-2.d0, 0.d0)
char_mat(3,14)=( 2.d0, 0.d0)
char_mat(3,15)=( 0.d0, 0.d0)
char_mat(3,16)=( 0.d0, 0.d0)
char_mat(3,17)=( 0.d0, 0.d0)
char_mat(3,18)=( 0.d0, 0.d0)
name_rap(4)="G_7- "
char_mat(4,1)=( 2.d0, 0.d0)
char_mat(4,2)=(-2.d0, 0.d0)
char_mat(4,3)=( 0.d0, 0.d0)
char_mat(4,4)=( 1.d0, 0.d0)
char_mat(4,5)=(-1.d0, 0.d0)
char_mat(4,6)=CMPLX( sqrt3, 0.d0)
char_mat(4,7)=CMPLX(-sqrt3, 0.d0)
char_mat(4,8)=( 0.d0, 0.d0)
char_mat(4,9)=( 0.d0, 0.d0)
char_mat(4,10)=(-2.d0, 0.d0)
char_mat(4,11)=( 2.d0, 0.d0)
char_mat(4,12)=( 0.d0, 0.d0)
char_mat(4,13)=(-1.d0, 0.d0)
char_mat(4,14)=( 1.d0, 0.d0)
char_mat(4,15)=CMPLX(-sqrt3, 0.d0)
char_mat(4,16)=CMPLX( sqrt3, 0.d0)
char_mat(4,17)=( 0.d0, 0.d0)
char_mat(4,18)=( 0.d0, 0.d0)
name_rap(5)="G_8- "
char_mat(5,1)=( 2.d0, 0.d0)
char_mat(5,2)=(-2.d0, 0.d0)
char_mat(5,3)=( 0.d0, 0.d0)
char_mat(5,4)=( 1.d0, 0.d0)
char_mat(5,5)=(-1.d0, 0.d0)
char_mat(5,6)=CMPLX(-sqrt3, 0.d0)
char_mat(5,7)=CMPLX( sqrt3, 0.d0)
char_mat(5,8)=( 0.d0, 0.d0)
char_mat(5,9)=( 0.d0, 0.d0)
char_mat(5,10)=(-2.d0, 0.d0)
char_mat(5,11)=( 2.d0, 0.d0)
char_mat(5,12)=( 0.d0, 0.d0)
char_mat(5,13)=(-1.d0, 0.d0)
char_mat(5,14)=( 1.d0, 0.d0)
char_mat(5,15)=CMPLX( sqrt3, 0.d0)
char_mat(5,16)=CMPLX(-sqrt3, 0.d0)
char_mat(5,17)=( 0.d0, 0.d0)
char_mat(5,18)=( 0.d0, 0.d0)
name_rap(6)="G_9- "
char_mat(6,1)=( 2.d0, 0.d0)
char_mat(6,2)=(-2.d0, 0.d0)
char_mat(6,3)=( 0.d0, 0.d0)
char_mat(6,4)=(-2.d0, 0.d0)
char_mat(6,5)=( 2.d0, 0.d0)
char_mat(6,6)=( 0.d0, 0.d0)
char_mat(6,7)=( 0.d0, 0.d0)
char_mat(6,8)=( 0.d0, 0.d0)
char_mat(6,9)=( 0.d0, 0.d0)
char_mat(6,10)=(-2.d0, 0.d0)
char_mat(6,11)=( 2.d0, 0.d0)
char_mat(6,12)=( 0.d0, 0.d0)
char_mat(6,13)=( 2.d0, 0.d0)
char_mat(6,14)=(-2.d0, 0.d0)
char_mat(6,15)=( 0.d0, 0.d0)
char_mat(6,16)=( 0.d0, 0.d0)
char_mat(6,17)=( 0.d0, 0.d0)
char_mat(6,18)=( 0.d0, 0.d0)
ELSEIF (code_group==24) THEN
!
! D_2d
!
nclass_ref=7
name_class(3)="C2 "
name_class1(3)="-C2 "
name_class(4)="2S4 "
name_class(5)="-2S4"
name_class(6)="2C2' "
name_class1(6)="-2C2'"
name_class(7)="2s_d "
name_class1(7)="-2s_d"
nrap_ref=2
name_rap(1)="G_6 X_6 W_6"
char_mat(1,1)=( 2.d0, 0.d0)
char_mat(1,2)=(-2.d0, 0.d0)
char_mat(1,3)=( 0.d0, 0.d0)
char_mat(1,4)=CMPLX( sqrt2, 0.d0)
char_mat(1,5)=CMPLX(-sqrt2, 0.d0)
char_mat(1,6)=( 0.d0, 0.d0)
char_mat(1,7)=( 0.d0, 0.d0)
name_rap(2)="G_7 X_7 W_7"
char_mat(2,1)=( 2.d0, 0.d0)
char_mat(2,2)=(-2.d0, 0.d0)
char_mat(2,3)=( 0.d0, 0.d0)
char_mat(2,4)=CMPLX(-sqrt2, 0.d0)
char_mat(2,5)=CMPLX( sqrt2, 0.d0)
char_mat(2,6)=( 0.d0, 0.d0)
char_mat(2,7)=( 0.d0, 0.d0)
ELSEIF (code_group==25) THEN
!
! D_3d
!
nclass_ref=12
name_class(3)="2C3 "
name_class(4)="-2C3"
name_class(5)="3s_v "
name_class(6)="-3s_v"
name_class(7)="i "
name_class(8)="-i "
name_class(9)="2S6 "
name_class(10)="-2S6"
name_class(11)="3C2'"
name_class(12)="-3C2'"
nrap_ref=6
name_rap(1)="G_4+ L_6+"
char_mat(1,1)=( 2.d0, 0.d0)
char_mat(1,2)=(-2.d0, 0.d0)
char_mat(1,4)=(-1.d0, 0.d0)
char_mat(1,5)=( 0.d0, 0.d0)
char_mat(1,6)=( 0.d0, 0.d0)
char_mat(1,7)=( 2.d0, 0.d0)
char_mat(1,8)=(-2.d0, 0.d0)
char_mat(1,10)=(-1.d0, 0.d0)
char_mat(1,11)=( 0.d0, 0.d0)
char_mat(1,12)=( 0.d0, 0.d0)
name_rap(2)="G_5+ L_4+"
char_mat(2,2)=(-1.d0, 0.d0)
char_mat(2,3)=(-1.d0, 0.d0)
char_mat(2,5)=( 0.d0, 1.d0)
char_mat(2,6)=( 0.d0,-1.d0)
char_mat(2,8)=(-1.d0, 0.d0)
char_mat(2,9)=(-1.d0, 0.d0)
char_mat(2,11)=( 0.d0, 1.d0)
char_mat(2,12)=( 0.d0,-1.d0)
name_rap(3)="G_6+ L_5+"
char_mat(3,2)=(-1.d0, 0.d0)
char_mat(3,3)=(-1.d0, 0.d0)
char_mat(3,5)=( 0.d0,-1.d0)
char_mat(3,6)=( 0.d0, 1.d0)
char_mat(3,8)=(-1.d0, 0.d0)
char_mat(3,9)=(-1.d0, 0.d0)
char_mat(3,11)=( 0.d0,-1.d0)
char_mat(3,12)=( 0.d0, 1.d0)
name_rap(4)="G_4- L_6-"
char_mat(4,1)=( 2.d0, 0.d0)
char_mat(4,2)=(-2.d0, 0.d0)
char_mat(4,4)=(-1.d0, 0.d0)
char_mat(4,5)=( 0.d0, 0.d0)
char_mat(4,6)=( 0.d0, 0.d0)
char_mat(4,7)=(-2.d0, 0.d0)
char_mat(4,8)=( 2.d0, 0.d0)
char_mat(4,9)=(-1.d0, 0.d0)
char_mat(4,11)=( 0.d0, 0.d0)
char_mat(4,12)=( 0.d0, 0.d0)
name_rap(5)="G_5- L_4-"
char_mat(5,2)=(-1.d0, 0.d0)
char_mat(5,3)=(-1.d0, 0.d0)
char_mat(5,5)=( 0.d0, 1.d0)
char_mat(5,6)=( 0.d0,-1.d0)
char_mat(5,7)=(-1.d0, 0.d0)
char_mat(5,10)=(-1.d0, 0.d0)
char_mat(5,11)=( 0.d0,-1.d0)
char_mat(5,12)=( 0.d0, 1.d0)
name_rap(6)="G_6- L_5-"
char_mat(6,2)=(-1.d0, 0.d0)
char_mat(6,3)=(-1.d0, 0.d0)
char_mat(6,5)=( 0.d0,-1.d0)
char_mat(6,6)=( 0.d0, 1.d0)
char_mat(6,7)=(-1.d0, 0.d0)
char_mat(6,10)=(-1.d0, 0.d0)
char_mat(6,11)=( 0.d0, 1.d0)
char_mat(6,12)=( 0.d0,-1.d0)
ELSEIF (code_group==26) THEN
!
! S_4
!
nclass_ref=8
name_class(3)=" S4 "
name_class(4)="-S4 "
name_class(5)=" C2 "
name_class(6)="-C2 "
name_class(7)=" S4^3"
name_class(8)="-S4^3"
nrap_ref=4
name_rap(1)="G_1 "
char_mat(1,3)=CMPLX( dsq2, dsq2)
char_mat(1,4)=CMPLX(-dsq2,-dsq2)
char_mat(1,5)=( 0.d0,-1.d0)
char_mat(1,6)=( 0.d0, 1.d0)
char_mat(1,7)=CMPLX(-dsq2, dsq2)
char_mat(1,8)=CMPLX( dsq2,-dsq2)
name_rap(2)="G_2 "
char_mat(2,3)=CMPLX( dsq2,-dsq2)
char_mat(2,4)=CMPLX(-dsq2, dsq2)
char_mat(2,5)=( 0.d0, 1.d0)
char_mat(2,6)=( 0.d0,-1.d0)
char_mat(2,7)=CMPLX(-dsq2,-dsq2)
char_mat(2,8)=CMPLX( dsq2, dsq2)
name_rap(3)="G_3 "
char_mat(3,3)=CMPLX(-dsq2,-dsq2)
char_mat(3,4)=CMPLX( dsq2, dsq2)
char_mat(3,5)=( 0.d0,-1.d0)
char_mat(3,6)=( 0.d0, 1.d0)
char_mat(3,7)=CMPLX( dsq2,-dsq2)
char_mat(3,8)=CMPLX(-dsq2, dsq2)
name_rap(4)="G_4 "
char_mat(4,3)=CMPLX(-dsq2, dsq2)
char_mat(4,4)=CMPLX( dsq2,-dsq2)
char_mat(4,5)=( 0.d0, 1.d0)
char_mat(4,6)=( 0.d0,-1.d0)
char_mat(4,7)=CMPLX( dsq2, dsq2)
char_mat(4,8)=CMPLX(-dsq2,-dsq2)
ELSEIF (code_group==27) THEN
!
! S_6
!
nclass_ref=12
name_class(3)="C3 "
name_class(4)="-C3 "
name_class(5)="C3^2"
name_class(6)="-C3^2"
name_class(7)=" i "
name_class(8)="-i "
name_class(9)="S6^5"
name_class(10)="-S6^5"
name_class(11)="S6"
name_class(12)="-S6"
nrap_ref=6
name_rap(1)="G_4+"
char_mat(1,3)=CMPLX( 0.5d0, sqr3d2 )
char_mat(1,4)=CMPLX(-0.5d0,-sqr3d2 )
char_mat(1,5)=CMPLX(-0.5d0, sqr3d2 )
char_mat(1,6)=CMPLX( 0.5d0,-sqr3d2 )
char_mat(1,8)=(-1.0d0, 0.d0 )
char_mat(1,9)=CMPLX( 0.5d0, sqr3d2 )
char_mat(1,10)=CMPLX(-0.5d0,-sqr3d2 )
char_mat(1,11)=CMPLX(-0.5d0, sqr3d2 )
char_mat(1,12)=CMPLX( 0.5d0,-sqr3d2 )
name_rap(2)="G_5+"
char_mat(2,3)=CMPLX( 0.5d0,-sqr3d2 )
char_mat(2,4)=CMPLX(-0.5d0, sqr3d2 )
char_mat(2,5)=CMPLX(-0.5d0,-sqr3d2 )
char_mat(2,6)=CMPLX( 0.5d0, sqr3d2 )
char_mat(2,8)=(-1.0d0, 0.d0 )
char_mat(2,9)=CMPLX( 0.5d0,-sqr3d2 )
char_mat(2,10)=CMPLX(-0.5d0, sqr3d2 )
char_mat(2,11)=CMPLX(-0.5d0,-sqr3d2 )
char_mat(2,12)=CMPLX( 0.5d0, sqr3d2 )
name_rap(3)="G_6+"
char_mat(3,3)=(-1.0d0, 0.d0 )
char_mat(3,6)=(-1.0d0, 0.d0 )
char_mat(3,8)=(-1.0d0, 0.d0 )
char_mat(3,9)=(-1.0d0, 0.d0 )
char_mat(3,12)=(-1.0d0, 0.d0 )
name_rap(4)="G_4-"
char_mat(4,3)=CMPLX( 0.5d0, sqr3d2 )
char_mat(4,4)=CMPLX(-0.5d0,-sqr3d2 )
char_mat(4,5)=CMPLX(-0.5d0, sqr3d2 )
char_mat(4,6)=CMPLX( 0.5d0,-sqr3d2 )
char_mat(4,7)=(-1.0d0, 0.d0 )
char_mat(4,9)=CMPLX(-0.5d0,-sqr3d2 )
char_mat(4,10)=CMPLX( 0.5d0, sqr3d2 )
char_mat(4,11)=CMPLX( 0.5d0,-sqr3d2 )
char_mat(4,12)=CMPLX(-0.5d0, sqr3d2 )
name_rap(5)="G_5-"
char_mat(5,3)=CMPLX( 0.5d0,-sqr3d2 )
char_mat(5,4)=CMPLX(-0.5d0, sqr3d2 )
char_mat(5,5)=CMPLX(-0.5d0,-sqr3d2 )
char_mat(5,6)=CMPLX( 0.5d0, sqr3d2 )
char_mat(5,7)=(-1.0d0, 0.d0 )
char_mat(5,9)=CMPLX(-0.5d0, sqr3d2 )
char_mat(5,10)=CMPLX( 0.5d0,-sqr3d2 )
char_mat(5,11)=CMPLX( 0.5d0, sqr3d2 )
char_mat(5,12)=CMPLX(-0.5d0,-sqr3d2 )
name_rap(6)="G_6-"
char_mat(6,3)=(-1.0d0, 0.d0 )
char_mat(6,6)=(-1.0d0, 0.d0 )
char_mat(6,7)=(-1.0d0, 0.d0 )
char_mat(6,10)=(-1.0d0, 0.d0 )
char_mat(6,11)=(-1.0d0, 0.d0 )
ELSEIF (code_group==28) THEN
!
! T
!
nclass_ref=7
name_class(3)="3C2 "
name_class1(3)="-3C2 "
name_class(4)=" 4C3 "
name_class(5)="-4C3 "
name_class(6)=" 4C3'"
name_class(7)="-4C3'"
nrap_ref=3
name_rap(1)="G_5 "
char_mat(1,1)=( 2.d0, 0.d0)
char_mat(1,2)=(-2.d0, 0.d0)
char_mat(1,3)=( 0.d0, 0.d0)
char_mat(1,5)=(-1.d0, 0.d0)
char_mat(1,7)=(-1.d0, 0.d0)
name_rap(2)="G_6 "
char_mat(2,1)=( 2.d0, 0.d0)
char_mat(2,2)=(-2.d0, 0.d0)
char_mat(2,3)=( 0.d0, 0.d0)
char_mat(2,4)=CMPLX( 0.5d0, sqr3d2)
char_mat(2,5)=CMPLX(-0.5d0,-sqr3d2)
char_mat(2,6)=CMPLX(-0.5d0, sqr3d2)
char_mat(2,7)=CMPLX( 0.5d0,-sqr3d2)
name_rap(3)="G_7 "
char_mat(3,1)=( 2.d0, 0.d0)
char_mat(3,2)=(-2.d0, 0.d0)
char_mat(3,3)=( 0.d0, 0.d0)
char_mat(3,4)=CMPLX( 0.5d0,-sqr3d2)
char_mat(3,5)=CMPLX(-0.5d0, sqr3d2)
char_mat(3,6)=CMPLX(-0.5d0,-sqr3d2)
char_mat(3,7)=CMPLX( 0.5d0, sqr3d2)
ELSEIF (code_group==29) THEN
!
! T_h
!
nclass_ref=14
name_class(3)=" 3C2 "
name_class1(3)="-3C2 "
name_class(4)=" 4C3 "
name_class(5)="-4C3 "
name_class(6)=" 4C3'"
name_class(7)="-4C3'"
name_class(8)="i "
name_class(9)="-i "
name_class(10)=" 3s_h"
name_class1(10)="-3s_h"
name_class(11)="4S6 "
name_class(12)="-4S6 "
name_class(13)=" 4S6'"
name_class(14)="-4S6'"
nrap_ref=6
name_rap(1)="G_5+"
char_mat(1,1)=( 2.d0, 0.d0)
char_mat(1,2)=(-2.d0, 0.d0)
char_mat(1,3)=( 0.d0, 0.d0)
char_mat(1,5)=(-1.d0, 0.d0)
char_mat(1,7)=(-1.d0, 0.d0)
char_mat(1,8)=( 2.d0, 0.d0)
char_mat(1,9)=(-2.d0, 0.d0)
char_mat(1,10)=( 0.d0, 0.d0)
char_mat(1,12)=(-1.d0, 0.d0)
char_mat(1,14)=(-1.d0, 0.d0)
name_rap(2)="G_6+"
char_mat(2,1)=( 2.d0, 0.d0)
char_mat(2,2)=(-2.d0, 0.d0)
char_mat(2,3)=( 0.d0, 0.d0)
char_mat(2,4)=CMPLX( 0.5d0, sqr3d2)
char_mat(2,5)=CMPLX(-0.5d0,-sqr3d2)
char_mat(2,6)=CMPLX(-0.5d0, sqr3d2)
char_mat(2,7)=CMPLX( 0.5d0,-sqr3d2)
char_mat(2,8)=( 2.d0, 0.d0)
char_mat(2,9)=(-2.d0, 0.d0)
char_mat(2,10)=( 0.d0, 0.d0)
char_mat(2,11)=CMPLX( 0.5d0, sqr3d2)
char_mat(2,12)=CMPLX(-0.5d0,-sqr3d2)
char_mat(2,13)=CMPLX(-0.5d0, sqr3d2)
char_mat(2,14)=CMPLX( 0.5d0,-sqr3d2)
name_rap(3)="G_7+"
char_mat(3,1)=( 2.d0, 0.d0)
char_mat(3,2)=(-2.d0, 0.d0)
char_mat(3,3)=( 0.d0, 0.d0)
char_mat(3,4)=CMPLX( 0.5d0,-sqr3d2)
char_mat(3,5)=CMPLX(-0.5d0, sqr3d2)
char_mat(3,6)=CMPLX(-0.5d0,-sqr3d2)
char_mat(3,7)=CMPLX( 0.5d0, sqr3d2)
char_mat(3,8)=( 2.d0, 0.d0)
char_mat(3,9)=(-2.d0, 0.d0)
char_mat(3,10)=( 0.d0, 0.d0)
char_mat(3,11)=CMPLX( 0.5d0,-sqr3d2)
char_mat(3,12)=CMPLX(-0.5d0, sqr3d2)
char_mat(3,13)=CMPLX(-0.5d0,-sqr3d2)
char_mat(3,14)=CMPLX( 0.5d0, sqr3d2)
name_rap(4)="G_5-"
char_mat(4,1)=( 2.d0, 0.d0)
char_mat(4,2)=(-2.d0, 0.d0)
char_mat(4,3)=( 0.d0, 0.d0)
char_mat(4,5)=(-1.d0, 0.d0)
char_mat(4,7)=(-1.d0, 0.d0)
char_mat(4,8)=(-2.d0, 0.d0)
char_mat(4,9)=( 2.d0, 0.d0)
char_mat(4,10)=( 0.d0, 0.d0)
char_mat(4,11)=(-1.d0, 0.d0)
char_mat(4,13)=(-1.d0, 0.d0)
name_rap(5)="G_6-"
char_mat(5,1)=( 2.d0, 0.d0)
char_mat(5,2)=(-2.d0, 0.d0)
char_mat(5,3)=( 0.d0, 0.d0)
char_mat(5,4)=CMPLX( 0.5d0, sqr3d2)
char_mat(5,5)=CMPLX(-0.5d0,-sqr3d2)
char_mat(5,6)=CMPLX(-0.5d0, sqr3d2)
char_mat(5,7)=CMPLX( 0.5d0,-sqr3d2)
char_mat(5,8)=(-2.d0, 0.d0)
char_mat(5,9)=( 2.d0, 0.d0)
char_mat(5,10)=( 0.d0, 0.d0)
char_mat(5,11)=CMPLX(-0.5d0,-sqr3d2)
char_mat(5,12)=CMPLX( 0.5d0, sqr3d2)
char_mat(5,13)=CMPLX( 0.5d0,-sqr3d2)
char_mat(5,14)=CMPLX(-0.5d0, sqr3d2)
name_rap(6)="G_7-"
char_mat(6,1)=( 2.d0, 0.d0)
char_mat(6,2)=(-2.d0, 0.d0)
char_mat(6,3)=( 0.d0, 0.d0)
char_mat(6,4)=CMPLX( 0.5d0,-sqr3d2)
char_mat(6,5)=CMPLX(-0.5d0, sqr3d2)
char_mat(6,6)=CMPLX(-0.5d0,-sqr3d2)
char_mat(6,7)=CMPLX( 0.5d0, sqr3d2)
char_mat(6,8)=(-2.d0, 0.d0)
char_mat(6,9)=( 2.d0, 0.d0)
char_mat(6,10)=( 0.d0, 0.d0)
char_mat(6,11)=CMPLX(-0.5d0, sqr3d2)
char_mat(6,12)=CMPLX( 0.5d0,-sqr3d2)
char_mat(6,13)=CMPLX( 0.5d0, sqr3d2)
char_mat(6,14)=CMPLX(-0.5d0,-sqr3d2)
ELSEIF (code_group==30) THEN
!
! T_d
!
nclass_ref=8
name_class(3)="8C3 "
name_class(4)="-8C3 "
name_class(5)=" 3C2 "
name_class1(5)="-3C2 "
name_class(6)="6s_d"
name_class1(6)="-6s_d"
name_class(7)="6S4 "
name_class(8)="-6S4 "
nrap_ref=3
name_rap(1)="G_6 P_6"
char_mat(1,1)=( 2.d0, 0.d0)
char_mat(1,2)=(-2.d0, 0.d0)
char_mat(1,4)=(-1.d0, 0.d0)
char_mat(1,5)=( 0.d0, 0.d0)
char_mat(1,6)=( 0.d0, 0.d0)
char_mat(1,7)=CMPLX( sqrt2, 0.d0)
char_mat(1,8)=CMPLX(-sqrt2, 0.d0)
name_rap(2)="G_7 P_7"
char_mat(2,1)=( 2.d0, 0.d0)
char_mat(2,2)=(-2.d0, 0.d0)
char_mat(2,4)=(-1.d0, 0.d0)
char_mat(2,5)=( 0.d0, 0.d0)
char_mat(2,6)=( 0.d0, 0.d0)
char_mat(2,7)=CMPLX(-sqrt2, 0.d0)
char_mat(2,8)=CMPLX( sqrt2, 0.d0)
name_rap(3)="G_8 P_8"
char_mat(3,1)=( 4.d0, 0.d0)
char_mat(3,2)=(-4.d0, 0.d0)
char_mat(3,3)=(-1.d0, 0.d0)
char_mat(3,5)=( 0.d0, 0.d0)
char_mat(3,6)=( 0.d0, 0.d0)
char_mat(3,7)=( 0.d0, 0.d0)
char_mat(3,8)=( 0.d0, 0.d0)
ELSEIF (code_group==31) THEN
!
! O
!
nclass_ref=8
name_class(3)="8C3 "
name_class(4)="-8C3 "
name_class(5)=" 3C2"
name_class1(5)="-3C2"
name_class(6)=" 6C2'"
name_class1(6)="-6C2'"
name_class(7)="6C4 "
name_class(8)="-6C4 "
nrap_ref=3
name_rap(1)="G_6 "
char_mat(1,1)=( 2.d0, 0.d0)
char_mat(1,2)=( -2.d0, 0.d0)
char_mat(1,4)=( -1.d0, 0.d0)
char_mat(1,5)=( 0.d0, 0.d0)
char_mat(1,6)=( 0.d0, 0.d0)
char_mat(1,7)=CMPLX( sqrt2, 0.d0)
char_mat(1,8)=CMPLX(-sqrt2, 0.d0)
name_rap(2)="G_7 "
char_mat(2,1)=( 2.d0, 0.d0)
char_mat(2,2)=( -2.d0, 0.d0)
char_mat(2,4)=( -1.d0, 0.d0)
char_mat(2,5)=( 0.d0, 0.d0)
char_mat(2,6)=( 0.d0, 0.d0)
char_mat(2,7)=CMPLX(-sqrt2, 0.d0)
char_mat(2,8)=CMPLX( sqrt2, 0.d0)
name_rap(3)="G_8 "
char_mat(3,1)=( 4.d0, 0.d0)
char_mat(3,2)=( -4.d0, 0.d0)
char_mat(3,3)=( -1.d0, 0.d0)
char_mat(3,5)=( 0.d0, 0.d0)
char_mat(3,6)=( 0.d0, 0.d0)
char_mat(3,7)=( 0.d0, 0.d0)
char_mat(3,8)=( 0.d0, 0.d0)
ELSEIF (code_group==32) THEN
!
! O_h
!
nclass_ref=16
name_class(3)="8C3 "
name_class(4)="-8C3 "
name_class(5)=" 3C2"
name_class1(5)="-3C2"
name_class(6)="6C4 "
name_class(7)="-6C4 "
name_class(8)=" 6C2'"
name_class1(8)="-6C2'"
name_class(9)="i "
name_class(10)="-i "
name_class(11)="8S6 "
name_class(12)="-8S6 "
name_class(13)=" 3s_h"
name_class1(13)="-3s_h"
name_class(14)="6S4 "
name_class(15)="-6S4 "
name_class(16)=" 6s_d"
name_class1(16)="-6s_d"
nrap_ref=6
name_rap(1)="G_6+ "
char_mat(1,1)=( 2.d0, 0.d0)
char_mat(1,2)=(-2.d0, 0.d0)
char_mat(1,4)=(-1.d0, 0.d0)
char_mat(1,5)=( 0.d0, 0.d0)
char_mat(1,6)=CMPLX( sqrt2, 0.d0)
char_mat(1,7)=CMPLX(-sqrt2, 0.d0)
char_mat(1,8)=( 0.d0, 0.d0)
char_mat(1,9)=( 2.d0, 0.d0)
char_mat(1,10)=(-2.d0, 0.d0)
char_mat(1,12)=(-1.d0, 0.d0)
char_mat(1,13)=( 0.d0, 0.d0)
char_mat(1,14)=CMPLX( sqrt2, 0.d0)
char_mat(1,15)=CMPLX(-sqrt2, 0.d0)
char_mat(1,16)=( 0.d0, 0.d0)
name_rap(2)="G_7+ "
char_mat(2,1)=( 2.d0, 0.d0)
char_mat(2,2)=(-2.d0, 0.d0)
char_mat(2,4)=(-1.d0, 0.d0)
char_mat(2,5)=( 0.d0, 0.d0)
char_mat(2,6)=CMPLX(-sqrt2, 0.d0)
char_mat(2,7)=CMPLX( sqrt2, 0.d0)
char_mat(2,8)=( 0.d0, 0.d0)
char_mat(2,9)=( 2.d0, 0.d0)
char_mat(2,10)=(-2.d0, 0.d0)
char_mat(2,12)=(-1.d0, 0.d0)
char_mat(2,13)=( 0.d0, 0.d0)
char_mat(2,14)=CMPLX(-sqrt2, 0.d0)
char_mat(2,15)=CMPLX( sqrt2, 0.d0)
char_mat(2,16)=( 0.d0, 0.d0)
name_rap(3)="G_8+ "
char_mat(3,1)=( 4.d0, 0.d0)
char_mat(3,2)=(-4.d0, 0.d0)
char_mat(3,3)=(-1.d0, 0.d0)
char_mat(3,5)=( 0.d0, 0.d0)
char_mat(3,6)=( 0.d0, 0.d0)
char_mat(3,7)=( 0.d0, 0.d0)
char_mat(3,8)=( 0.d0, 0.d0)
char_mat(3,9)=( 4.d0, 0.d0)
char_mat(3,10)=(-4.d0, 0.d0)
char_mat(3,11)=(-1.d0, 0.d0)
char_mat(3,13)=( 0.d0, 0.d0)
char_mat(3,14)=( 0.d0, 0.d0)
char_mat(3,15)=( 0.d0, 0.d0)
char_mat(3,16)=( 0.d0, 0.d0)
name_rap(4)="G_6- "
char_mat(4,1)=( 2.d0, 0.d0)
char_mat(4,2)=(-2.d0, 0.d0)
char_mat(4,4)=(-1.d0, 0.d0)
char_mat(4,5)=( 0.d0, 0.d0)
char_mat(4,6)=CMPLX(sqrt2, 0.d0)
char_mat(4,7)=CMPLX(-sqrt2, 0.d0)
char_mat(4,8)=( 0.d0, 0.d0)
char_mat(4,9)=(-2.d0, 0.d0)
char_mat(4,10)=( 2.d0, 0.d0)
char_mat(4,11)=(-1.d0, 0.d0)
char_mat(4,13)=( 0.d0, 0.d0)
char_mat(4,14)=CMPLX(-sqrt2, 0.d0)
char_mat(4,15)=CMPLX( sqrt2, 0.d0)
char_mat(4,16)=( 0.d0, 0.d0)
name_rap(5)="G_7- "
char_mat(5,1)=( 2.d0, 0.d0)
char_mat(5,2)=(-2.d0, 0.d0)
char_mat(5,4)=(-1.d0, 0.d0)
char_mat(5,5)=( 0.d0, 0.d0)
char_mat(5,6)=CMPLX(-sqrt2, 0.d0)
char_mat(5,7)=CMPLX( sqrt2, 0.d0)
char_mat(5,8)=( 0.d0, 0.d0)
char_mat(5,9)=(-2.d0, 0.d0)
char_mat(5,10)=( 2.d0, 0.d0)
char_mat(5,11)=(-1.d0, 0.d0)
char_mat(5,13)=( 0.d0, 0.d0)
char_mat(5,14)=CMPLX( sqrt2, 0.d0)
char_mat(5,15)=CMPLX(-sqrt2, 0.d0)
char_mat(5,16)=( 0.d0, 0.d0)
name_rap(6)="G_8- "
char_mat(6,1)=( 4.d0, 0.d0)
char_mat(6,2)=(-4.d0, 0.d0)
char_mat(6,3)=(-1.d0, 0.d0)
char_mat(6,5)=( 0.d0, 0.d0)
char_mat(6,6)=( 0.d0, 0.d0)
char_mat(6,7)=( 0.d0, 0.d0)
char_mat(6,8)=( 0.d0, 0.d0)
char_mat(6,9)=(-4.d0, 0.d0)
char_mat(6,10)=( 4.d0, 0.d0)
char_mat(6,12)=(-1.d0, 0.d0)
char_mat(6,13)=( 0.d0, 0.d0)
char_mat(6,14)=( 0.d0, 0.d0)
char_mat(6,15)=( 0.d0, 0.d0)
char_mat(6,16)=( 0.d0, 0.d0)
ELSE
CALL errore('set_irr_rap_so','code number not allowed',1)
END IF
RETURN
END SUBROUTINE set_irr_rap_so
!--------------------------------------------------------------------------
FUNCTION is_complex_so(code)
!--------------------------------------------------------------------------
! This function receives a code of the group and provide .true. or
! .false. if the double group HAS or HAS NOT complex irreducible
! representations.
! The order is the following:
!
! 1 "C_1 " F 11 "D_6 " F 21 "D_3h" F 31 "O " F
! 2 "C_i " F 12 "C_2v" F 22 "D_4h" F 32 "O_h " F
! 3 "C_s " T 13 "C_3v" T 23 "D_6h" F
! 4 "C_2 " T 14 "C_4v" F 24 "D_2d" F
! 5 "C_3 " T 15 "C_6v" F 25 "D_3d" T
! 6 "C_4 " T 16 "C_2h" T 26 "S_4 " T
! 7 "C_6 " T 17 "C_3h" T 27 "S_6 " T
! 8 "D_2 " F 18 "C_4h" T 28 "T " T
! 9 "D_3 " T 19 "C_6h" T 29 "T_h " T
! 10 "D_4 " F 20 "D_2h" F 30 "T_d " F
!
IMPLICIT NONE
INTEGER :: code
LOGICAL :: is_complex_so
LOGICAL :: complex_aux(32)
data complex_aux / .FALSE., .FALSE., .TRUE., .TRUE., .TRUE. , &
.TRUE. , .TRUE. , .FALSE., .TRUE., .FALSE., &
.FALSE., .FALSE., .TRUE., .FALSE., .FALSE., &
.TRUE., .TRUE. , .TRUE., .TRUE., .FALSE., &
.FALSE., .FALSE., .FALSE., .FALSE., .TRUE., &
.TRUE. , .TRUE. , .TRUE. , .TRUE. , .FALSE., &
.FALSE., .FALSE. /
IF (code < 1 .OR. code > 32 ) CALL errore('is_complex', &
'code is out of range',1)
is_complex_so= complex_aux(code)
RETURN
END FUNCTION is_complex_so
!
!----------------------------------------------------------------------------
SUBROUTINE write_group_info(flag)
!----------------------------------------------------------------------------
!
! This routine writes on output the main information on the point group
! If flag is .false. writes only the character table. If flag is .true.
! writes also the elements of each class.
!
!
USE rap_point_group, ONLY : code_group, nclass, nelem, elem, which_irr, &
char_mat, name_rap, name_class, gname
USE rap_point_group_so, ONLY : nrap, nelem_so, elem_so, has_e, &
which_irr_so, char_mat_so, name_rap_so, &
name_class_so, d_spin, name_class_so1
USE rap_point_group_is, ONLY : code_group_is, gname_is
USE spin_orb, ONLY : domag
USE noncollin_module, ONLY : noncolin
USE io_global, ONLY : stdout
IMPLICIT NONE
More patches by Axel: all occurrences of "index" replaced by "idx". "index" is an instrinsic and shouldn't be used as a variable. control-M characters removed from qexml.f90 git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3585 c92efa57-630b-4861-b058-cf58834340f0
2006-12-01 22:41:55 +08:00
INTEGER :: iclass, irot, i, idx
Now bands.x can classify the bands according to the irreducible representation of the small group of k. k points on the border of the Brillouin zone of systems with non symmorphic space groups are not dealt with. Spin-orbit case included. Find_mode_sym extended to all the q points, with the same limitations as the bands. (still experimental). git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3330 c92efa57-630b-4861-b058-cf58834340f0
2006-08-23 01:01:13 +08:00
LOGICAL :: is_complex, is_complex_so, flag
IF (noncolin) THEN
IF (domag) THEN
WRITE(stdout,'(/,5x,"the magnetic double point group is ", &
& a11," [",a11,"]")') &
gname, gname_is
WRITE(stdout,'(5x,"using the double point group ",a11)') &
gname_is
ELSE
WRITE(stdout,'(/,5x,"double point group ",a11)') gname
END IF
WRITE(stdout,'(5x, "there are", i3," classes and",i3, &
Missing continuation "&" added git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3370 c92efa57-630b-4861-b058-cf58834340f0
2006-09-09 01:13:41 +08:00
& " irreducible representations")') nclass, nrap
Now bands.x can classify the bands according to the irreducible representation of the small group of k. k points on the border of the Brillouin zone of systems with non symmorphic space groups are not dealt with. Spin-orbit case included. Find_mode_sym extended to all the q points, with the same limitations as the bands. (still experimental). git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3330 c92efa57-630b-4861-b058-cf58834340f0
2006-08-23 01:01:13 +08:00
ELSE
WRITE(stdout,'(/,5x,"point group ",a11)') gname
WRITE(stdout,'(5x, "there are", i3," classes")') nclass
ENDIF
WRITE(stdout,'(5x, "the character table:")')
IF (noncolin) THEN
WRITE(stdout,'(/,7x,12(a5,1x))') (name_class_so(irot), &
irot=1,MIN(12,nclass))
WRITE(stdout,'(7x,12(a5,1x))') (name_class_so1(irot), &
irot=1,MIN(12,nclass))
DO iclass=1,nrap
WRITE(stdout,'(a5,12f6.2)') name_rap_so(iclass), &
(REAL(char_mat_so(iclass,irot)), irot=1,MIN(nclass,12))
END DO
IF (nclass > 12 ) THEN
WRITE(stdout,'(/,7x,12(a5,1x))') (name_class_so(irot), &
irot=13,nclass)
WRITE(stdout,'(7x,12(a5,1x))') (name_class_so1(irot), &
irot=13,nclass)
DO iclass=1,nrap
WRITE(stdout,'(a5,12f6.2)') name_rap_so(iclass), &
(REAL(char_mat_so(iclass,irot)), irot=13,nclass)
END DO
END IF
More patches by Axel: all occurrences of "index" replaced by "idx". "index" is an instrinsic and shouldn't be used as a variable. control-M characters removed from qexml.f90 git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3585 c92efa57-630b-4861-b058-cf58834340f0
2006-12-01 22:41:55 +08:00
idx=code_group
IF (noncolin.and.domag) idx=code_group_is
IF (is_complex_so(idx)) THEN
Now bands.x can classify the bands according to the irreducible representation of the small group of k. k points on the border of the Brillouin zone of systems with non symmorphic space groups are not dealt with. Spin-orbit case included. Find_mode_sym extended to all the q points, with the same limitations as the bands. (still experimental). git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3330 c92efa57-630b-4861-b058-cf58834340f0
2006-08-23 01:01:13 +08:00
WRITE(stdout,'(/,5x,"imaginary part")')
WRITE(stdout,'(/,7x,12(a5,1x))') (name_class_so(irot), &
irot=1,MIN(12,nclass))
WRITE(stdout,'(7x,12(a5,1x))') (name_class_so1(irot), &
irot=1,MIN(12,nclass))
DO iclass=1,nrap
WRITE(stdout,'(a5,12f6.2)') name_rap_so(iclass), &
(AIMAG(char_mat_so(iclass,irot)),irot=1, MIN(nclass,12))
END DO
IF (nclass > 12 ) THEN
WRITE(stdout,'(/,7x,12(a5,1x))') (name_class_so(irot), &
irot=13,nclass)
WRITE(stdout,'(7x,12(a5,1x))') (name_class_so1(irot), &
irot=13,nclass)
DO iclass=1,nrap
WRITE(stdout,'(a5,12f6.2)') name_rap_so(iclass), &
(AIMAG(char_mat_so(iclass,irot)),irot=13, nclass)
END DO
END IF
END IF
IF (flag) THEN
WRITE(stdout,'(/5x, "the symmetry operations in each class:")')
DO iclass=1,nclass
WRITE(stdout,'(5x,2a5,12i5)') &
name_class_so(which_irr_so(iclass)), &
name_class_so1(which_irr_so(iclass)), &
(elem_so(i,iclass)*has_e(i,iclass), i=1,nelem_so(iclass))
ENDDO
ENDIF
ELSE
WRITE(stdout,'(/,7x,12(a5,1x))') (name_class(irot),irot=1,nclass)
DO iclass=1,nclass
WRITE(stdout,'(a5,12f6.2)') name_rap(iclass), &
(REAL(char_mat(iclass,irot)),irot=1,nclass)
ENDDO
More patches by Axel: all occurrences of "index" replaced by "idx". "index" is an instrinsic and shouldn't be used as a variable. control-M characters removed from qexml.f90 git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3585 c92efa57-630b-4861-b058-cf58834340f0
2006-12-01 22:41:55 +08:00
idx=code_group
IF (noncolin.and.domag) idx=code_group_is
IF (is_complex(idx)) THEN
Now bands.x can classify the bands according to the irreducible representation of the small group of k. k points on the border of the Brillouin zone of systems with non symmorphic space groups are not dealt with. Spin-orbit case included. Find_mode_sym extended to all the q points, with the same limitations as the bands. (still experimental). git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@3330 c92efa57-630b-4861-b058-cf58834340f0
2006-08-23 01:01:13 +08:00
WRITE(stdout,'(5x,"imaginary part")')
DO iclass=1,nclass
WRITE(stdout,'(a5,12f6.2)') name_rap(iclass), &
(AIMAG(char_mat(iclass,irot)),irot=1,nclass)
ENDDO
ENDIF
IF (flag) THEN
WRITE(stdout,'(/5x, "the symmetry operations in each class:")')
DO iclass=1,nclass
WRITE(stdout,'(5x,a5,12i5)') name_class(which_irr(iclass)), &
(elem(i,iclass), i=1,nelem(iclass))
ENDDO
END IF
END IF
RETURN
END SUBROUTINE write_group_info
!---------------------------------------------------------------------------
SUBROUTINE find_u(s,u)
!---------------------------------------------------------------------------
!
! This subroutine receives as input a 3x3 rotation matrix s, and gives
! as output the matrix u which represents the same rotation in the spin
! space. Only one of the two u matrices is given. See below for the
! definition of the sign.
!
USE kinds, ONLY : DP
USE constants, ONLY : pi
IMPLICIT NONE
REAL(DP) :: s(3,3)
COMPLEX(DP) :: u(2,2)
REAL(DP), PARAMETER :: eps=1.d-8
REAL(DP) :: det, saux(3,3), ax(3), angle, cosa, sina, angle_rot
!
! For consistency check uncomment here
!
!COMPLEX(DP) :: a, as, b, bs
!REAL(DP) :: r(3,3), r1(3,3), diff
det = s(1,1) * ( s(2,2) * s(3,3) - s(3,2) * s(2,3) )- &
s(1,2) * ( s(2,1) * s(3,3) - s(3,1) * s(2,3) )+ &
s(1,3) * ( s(2,1) * s(3,2) - s(3,1) * s(2,2) )
!
! inversion has no effect in spin space, so improper rotations are
! multiplied by inversion
!
IF (ABS(det+1.d0) < eps) THEN
saux=-s
ELSE
saux=s
ENDIF
!
! Check for identity or inversion
!
IF ((ABS(saux(1,1)-1.d0) < eps).AND. &
(ABS(saux(2,2)-1.d0) < eps).AND. &
(ABS(saux(3,3)-1.d0) < eps).AND. &
(ABS(saux(1,2)) < eps).AND.(ABS(saux(2,1)) < eps) &
.AND.(ABS(saux(2,3)) < eps).AND. &
(ABS(saux(3,2)) < eps).AND.(ABS(saux(1,3)) < eps) &
.AND.(ABS(saux(3,1)) < eps)) THEN
u(1,1)=(1.d0,0.d0)
u(1,2)=(0.d0,0.d0)
u(2,1)=(0.d0,0.d0)
u(2,2)=(1.d0,0.d0)
RETURN
ENDIF
!
! Find the rotation axis and the rotation angle
!
CALL versor(saux,ax)
angle=angle_rot(saux)
!write(6,'(3f12.5,5x,f12.5)') ax(1), ax(2), ax(3), angle
angle=0.5d0*angle*pi/180.d0
cosa=COS(angle)
sina=SIN(angle)
!write(6,'(2f12.5)') cosa, sina
!
! set the spin space rotation matrix elements
!
u(1,1)=CMPLX(cosa,-ax(3)*sina)
u(1,2)=CMPLX(-ax(2)*sina, -ax(1)*sina)
u(2,1)=-CONJG(u(1,2))
u(2,2)=CONJG(u(1,1))
!
! To each 3x3 rotation one can associate two 2x2 rotation matrices in spin
! space. This function returns the U matrix with positive cosa term
!
IF (cosa < -eps ) u=-u
IF (ABS(cosa) < eps) THEN
!
! Special case when cosa=0. For this rotation we must take the negative sign.
!
IF (ax(1)*ax(3) < -eps) u=-u
ENDIF
!
! Here compute the 3x3 rotation matrix starting form the axis, angle
! or from the rotation in spin space for consistency check.
!
!angle=angle*2.d0
!cosa=COS(angle)
!sina=SIN(angle)
!r1(1,1)=1.d0+(1.d0-cosa)*(ax(1)**2-1)
!r1(1,2)=-ax(3)*sina+(1.d0-cosa)*ax(1)*ax(2)
!r1(1,3)=ax(2)*sina+(1.d0-cosa)*ax(1)*ax(3)
!r1(2,1)=ax(3)*sina+(1.d0-cosa)*ax(1)*ax(2)
!r1(2,2)=1.d0+(1.d0-cosa)*(ax(2)**2-1)
!r1(2,3)=-ax(1)*sina+(1.d0-cosa)*ax(2)*ax(3)
!r1(3,1)=-ax(2)*sina+(1.d0-cosa)*ax(1)*ax(3)
!r1(3,2)=ax(1)*sina+(1.d0-cosa)*ax(2)*ax(3)
!r1(3,3)=1.d0+(1.d0-cosa)*(ax(3)**2-1)
!a=u(1,1)
!as=u(2,2)
!b=u(1,2)
!bs=-u(2,1)
!r(1,1)=0.5d0*(a**2+as**2-b**2-bs**2)
!r(1,2)=0.5d0*(0.d0,1.d0)*(as**2+bs**2-a**2-b**2)
!r(1,3)=-(a*b+as*bs)
!r(2,1)=-0.5d0*(0.d0,1.d0)*(as**2-a**2+b**2-bs**2)
!r(2,2)=0.5d0*(a**2+b**2+as**2+bs**2)
!r(2,3)=(0.d0,1.d0)*(as*bs-a*b)
!r(3,1)=(bs*a+as*b)
!r(3,2)=(0.d0,1.d0)*(as*b-bs*a)
!r(3,3)=(a*as-b*bs)
!diff=ABS(r(1,1)-saux(1,1))+ &
! ABS(r(1,2)-saux(1,2))+ &
! ABS(r(1,3)-saux(1,3))+ &
! ABS(r(2,1)-saux(2,1))+ &
! ABS(r(2,2)-saux(2,2))+ &
! ABS(r(2,3)-saux(2,3))+ &
! ABS(r(3,1)-saux(3,1))+ &
! ABS(r(3,2)-saux(3,2))+ &
! ABS(r(3,3)-saux(3,3))
!write(6,*) diff
!write(6,'(3f15.5)') r1(1,1),r1(1,2),r1(1,3)
!write(6,'(3f15.5)') r1(2,1),r1(2,2),r1(2,3)
!write(6,'(3f15.5)') r1(3,1),r1(3,2),r1(3,3)
!write(6,*)
!write(6,'(3f15.5)') r(1,1),r(1,2),r(1,3)
!write(6,'(3f15.5)') r(2,1),r(2,2),r(2,3)
!write(6,'(3f15.5)') r(3,1),r(3,2),r(3,3)
!write(6,*)
!write(6,'(4f15.5)') u(1,1),u(1,2)
!write(6,'(4f15.5)') u(2,1),u(2,2)
!
RETURN
END SUBROUTINE find_u
!-----------------------------------------------------------------------------
FUNCTION set_e(hase,ind)
!-----------------------------------------------------------------------------
IMPLICIT NONE
INTEGER :: set_e, hase, ind
IF (hase==-1) THEN
set_e=ind+1
ELSE
set_e=ind
ENDIF
RETURN
END FUNCTION set_e
!-----------------------------------------------------------------------------
SUBROUTINE check_tgroup(nsym,a,b)
!-----------------------------------------------------------------------------
!
! This subroutine receives a set of 2x2 and 3x3 rotation matrices and
! checks if they are a group.
!
USE kinds, ONLY : DP
IMPLICIT NONE
COMPLEX(DP) :: a(2,2,48), c(2,2), a1(2,2), a2(2,2), a3(2,2)
REAL(DP) :: b(3,3,48), d(3,3), b1(3,3), b2(3,3), b3(3,3)
INTEGER :: nsym, done
LOGICAL :: compare_mat_so
INTEGER :: i, j, k
DO i=1,nsym
a1(:,:)=a(:,:,i)
b1(:,:)=b(:,:,i)
DO j=1,nsym
a2(:,:)=a(:,:,j)
b2(:,:)=b(:,:,j)
c=MATMUL(a1,a2)
d=MATMUL(b1,b2)
done=0
do k=1,nsym
a3(:,:)=a(:,:,k)
b3(:,:)=b(:,:,k)
IF (compare_mat_so(d,c,b3,a3)) THEN
done=done+1
ENDIF
ENDDO
IF (done.ne.1) write(6,*) 'problem, i,j',i,j
END DO
END DO
RETURN
END SUBROUTINE check_tgroup