scnc
/
quantum-espresso
mirror of https://gitlab.com/QEF/q-e.git
1
0
Fork 0
Code Issues Packages Projects Releases Wiki Activity
quantum-espresso/PW/divide_class.f90

2621 lines
62 KiB
Fortran
Raw Blame History

!
! 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(code_group,nrot,smat,nclass,nelem,elem,which_irr)
!-----------------------------------------------------------------------------
!
! This subroutine receives as input a set of nrot 3x3 matrices smat, which
! are assumed to be the operations of the point group given by code_group.
! smat are in cartesian coordinates.
! This routine divide the group in classes and find:
!
! nclass the number of classes of the 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
! 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. NB: changing the order of
! the elements in the character table must be reflected in
! a change to which_irr. Presently the character tables
! are those given by P.W. Atkins, M.S. Child, and
! C.S.G. Phillips, "Tables for group theory".
! 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(12), & ! The elements of each class
elem(8,12), & ! Which elements in the smat list for each class
which_irr(12) ! See above
REAL(DP) :: smat(3,3,nrot), cmat(3,3), ax(3), ars
INTEGER :: done(48), irot, jrot, krot, iclass, i
INTEGER :: tipo_sym, ipol, axis, axis1, axis2, ts
REAL(DP), PARAMETER :: eps = 1.d-7
REAL(DP) :: angle_rot, angle_rot_s
LOGICAL :: compare_mat, is_axis, first, first1, done_ax(6)
!
! Divide the group in classes.
!
nclass=0
nelem=0
done=0
DO irot=1,nrot
IF (done(irot)==0) THEN
nclass=nclass+1
DO jrot=1,nrot
CALL coniug_mat(smat(1,1,jrot),smat(1,1,irot),cmat)
DO krot=1,nrot
IF (compare_mat(cmat,smat(1,1,krot)).AND.done(krot)==0) THEN
nelem(nclass)=nelem(nclass)+1
elem(nelem(nclass),nclass)=krot
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,
! so we must make different things for different groups.
!
which_irr(1)=1
IF (code_group==1) THEN
!
! C_1
!
ELSEIF (code_group==2.OR.code_group==3.OR.code_group==4) THEN
!
! C_i, C_s, C_2
!
which_irr(2)=2
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 (ABS(angle_rot(smat(1,1,elem(1,iclass)))-120.d0)<eps) THEN
which_irr(iclass)=2
ELSE
which_irr(iclass)=3
ENDIF
ENDDO
ELSEIF (code_group==6) THEN
!
! C_4
!
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==4) THEN
which_irr(iclass)=3
ELSEIF (ts==3) THEN
ars=angle_rot(smat(1,1,elem(1,iclass)))
IF (ABS(ars-90.d0)<eps) THEN
which_irr(iclass)=2
ELSEIF (ABS(ars-270.d0)<eps) THEN
which_irr(iclass)=4
ELSE
CALL errore('divide_class','wrong angle',1)
ENDIF
ELSE
CALL errore('divide_class','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==4) THEN
which_irr(iclass)=4
ELSEIF (ts==3) THEN
ars=angle_rot(smat(1,1,elem(1,iclass)))
IF (ABS(ars-60.d0)<eps) THEN
which_irr(iclass)=2
ELSEIF (ABS(ars-120.d0)<eps) THEN
which_irr(iclass)=3
ELSEIF (ABS(ars-240.d0)<eps) THEN
which_irr(iclass)=5
ELSEIF (ABS(ars-300.d0)<eps) THEN
which_irr(iclass)=6
ELSE
CALL errore('divide_class','wrong angle',1)
ENDIF
ELSE
CALL errore('divide_class','wrong sym_type',1)
ENDIF
ENDDO
ELSEIF (code_group==8) THEN
!
! D_2
!
DO iclass=2,nclass
which_irr(iclass)=iclass
ENDDO
ELSEIF (code_group==9) THEN
!
! D_3
!
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==4) THEN
which_irr(iclass)=3
ELSEIF (ts==3) THEN
which_irr(iclass)=2
ELSE
CALL errore('divide_class','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)=2
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
IF (axis==0) call errore('divide_class','unknown D_4 axis ',1)
ENDIF
END DO
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==4) THEN
CALL versor(smat(1,1,elem(1,iclass)),ax)
IF (is_axis(ax,axis)) THEN
which_irr(iclass)=3
ELSEIF (is_axis(ax,axis1).or.is_axis(ax,axis2)) THEN
which_irr(iclass)=4
ELSE
which_irr(iclass)=5
END IF
ELSEIF (ts.ne.3) THEN
CALL errore('divide_class','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==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)=2
ELSE
which_irr(iclass)=3
ENDIF
ELSEIF (ts==4) THEN
CALL versor(smat(1,1,elem(1,iclass)),ax)
IF (is_axis(ax,3)) THEN
which_irr(iclass)=4
ELSE
IF (first) THEN
which_irr(iclass)=5
first=.false.
ELSE
which_irr(iclass)=6
END IF
END IF
ELSE
CALL errore('divide_class','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==4) THEN
which_irr(iclass)=2
ELSEIF (ts==5.and.first) THEN
which_irr(iclass)=3
first=.false.
ELSE
which_irr(iclass)=4
ENDIF
ENDDO
ELSEIF (code_group==13) THEN
!
! C_3v
!
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==3) THEN
which_irr(iclass)=2
ELSEIF (ts==5) THEN
which_irr(iclass)=3
ELSE
CALL errore('divide_class','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==3) 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==15) THEN
!
! C_6v
!
first=.true.
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
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)=2
ELSE
which_irr(iclass)=3
ENDIF
ELSEIF (ts==4) THEN
which_irr(iclass)=4
ELSEIF (ts==5.and.first) THEN
which_irr(iclass)=5
first=.false.
ELSE
which_irr(iclass)=6
ENDIF
ENDDO
ELSEIF (code_group==16) THEN
!
! C_2h
!
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==4) THEN
which_irr(iclass)=2
ELSEIF (ts==2) THEN
which_irr(iclass)=3
ELSEIF (ts==5) THEN
which_irr(iclass)=4
ELSE
CALL errore('divide_class','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==3) THEN
IF (ABS(angle_rot(smat(1,1,elem(1,iclass)))-120.d0)<eps) THEN
which_irr(iclass)=2
ELSE
which_irr(iclass)=3
END IF
ELSEIF (ts==5) THEN
which_irr(iclass)=4
ELSEIF (ts==6) THEN
IF (ABS(angle_rot_s(smat(1,1,elem(1,iclass)))-120.d0)<eps) THEN
which_irr(iclass)=5
ELSE
which_irr(iclass)=6
END IF
ELSE
call errore('divide_class','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==3) THEN
IF (angle_rot(smat(1,1,elem(1,iclass)))-90.d0<eps) THEN
which_irr(iclass)=2
ELSE
which_irr(iclass)=4
END IF
ELSEIF (ts==4) THEN
which_irr(iclass)=3
ELSEIF (ts==2) THEN
which_irr(iclass)=5
ELSEIF (ts==5) THEN
which_irr(iclass)=7
ELSEIF (ts==6) THEN
IF (angle_rot_s(smat(1,1,elem(1,iclass)))-90.d0<eps) THEN
which_irr(iclass)=8
ELSE
which_irr(iclass)=6
END IF
ELSE
CALL errore('divide_class','wrong operation',1)
ENDIF
ENDDO
ELSEIF (code_group==19) THEN
!
! C_6h
!
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==3) THEN
ars=angle_rot(smat(1,1,elem(1,iclass)))
IF (ABS(ars-60.d0)<eps) THEN
which_irr(iclass)=2
ELSEIF (ABS(ars-120.d0)<eps) THEN
which_irr(iclass)=3
ELSEIF (ABS(ars-240.d0)<eps) THEN
which_irr(iclass)=5
ELSEIF (ABS(ars-300.d0)<eps) THEN
which_irr(iclass)=6
END IF
ELSEIF (ts==4) THEN
which_irr(iclass)=4
ELSEIF (ts==2) THEN
which_irr(iclass)=7
ELSEIF (ts==5) THEN
which_irr(iclass)=10
ELSEIF (ts==6) THEN
ars=angle_rot_s(smat(1,1,elem(1,iclass)))
IF (ABS(ars-60.d0)<eps) THEN
which_irr(iclass)=11
ELSEIF (ABS(ars-120.d0)<eps) THEN
which_irr(iclass)=12
ELSEIF (ABS(ars-240.d0)<eps) THEN
which_irr(iclass)=8
ELSEIF (ABS(ars-300.d0)<eps) THEN
which_irr(iclass)=9
END IF
ELSE
call errore('divide_class','wrong operation',1)
ENDIF
ENDDO
ELSEIF (code_group==20) THEN
!
! D_2h
!
! mirror_axis gives the normal to the mirror plane
!
done_ax=.TRUE.
DO iclass=2,nclass
ts=tipo_sym(smat(1,1,elem(1,iclass)))
IF (ts==4) THEN
CALL versor(smat(1,1,elem(1,iclass)),ax)
IF (is_axis(ax,3)) THEN
which_irr(iclass)=2
done_ax(1)=.FALSE.
ELSE IF (is_axis(ax,2)) THEN
which_irr(iclass)=3
done_ax(2)=.FALSE.
ELSE IF (is_axis(ax,1)) THEN
which_irr(iclass)=4
done_ax(3)=.FALSE.
ELSE
DO i=1,3
IF (done_ax(i)) THEN
which_irr(iclass)=i+1
done_ax(i)=.FALSE.
GOTO 100
END IF
END DO
100 CONTINUE
END IF
ELSEIF (ts==2) THEN
which_irr(iclass)=5
ELSEIF (ts==5) THEN
CALL mirror_axis(smat(1,1,elem(1,iclass)),ax)
IF (is_axis(ax,3)) THEN
which_irr(iclass)=6
done_ax(4)=.FALSE.
ELSE IF (is_axis(ax,2)) THEN
which_irr(iclass)=7
done_ax(5)=.FALSE.
ELSE IF (is_axis(ax,1)) THEN
which_irr(iclass)=8
done_ax(6)=.FALSE.
ELSE
DO i=4,6
IF (done_ax(i)) THEN
which_irr(iclass)=i+2
done_ax(i)=.FALSE.
GOTO 120
END IF
END DO
120 CONTINUE
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==3) THEN
which_irr(iclass)=2
ELSE IF (ts==4) THEN
which_irr(iclass)=3
ELSE IF (ts==5) THEN
IF (nelem(iclass)>1) THEN
which_irr(iclass)=6
ELSE
which_irr(iclass)=4
END IF
ELSE IF (ts==6) THEN
which_irr(iclass)=5
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)=2
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','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==4) THEN
CALL versor(smat(1,1,elem(1,iclass)),ax)
IF (is_axis(ax,axis)) THEN
which_irr(iclass)=3
ELSE
IF (first) THEN
which_irr(iclass)=4
first=.FALSE.
ELSE
which_irr(iclass)=5
END IF
END IF
ELSEIF (ts==2) THEN
which_irr(iclass)=6
ELSEIF (ts==5) THEN
CALL mirror_axis(smat(1,1,elem(1,iclass)),ax)
IF (is_axis(ax,axis)) THEN
which_irr(iclass)=8
ELSE
IF (first1) THEN
which_irr(iclass)=9
first1=.FALSE.
ELSE
which_irr(iclass)=10
END IF
END IF
ELSEIF (ts==6) THEN
which_irr(iclass)=7
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==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)=2
ELSE
which_irr(iclass)=3
END IF
ELSE IF (ts==4) THEN
IF (nelem(iclass)==1) THEN
which_irr(iclass)=4
ELSE
IF (first) THEN
which_irr(iclass)=5
first=.FALSE.
ELSE
which_irr(iclass)=6
END IF
END IF
ELSE IF (ts==2) THEN
which_irr(iclass)=7
ELSE IF (ts==5) THEN
IF (nelem(iclass)==1) THEN
which_irr(iclass)=10
ELSE
IF (first1) THEN
which_irr(iclass)=11
first1=.FALSE.
ELSE
which_irr(iclass)=12
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)=9
ELSE
which_irr(iclass)=8
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==6) THEN
which_irr(iclass)=2
ELSE IF (ts==4) THEN
IF (nelem(iclass)==1) THEN
which_irr(iclass)=3
ELSE
which_irr(iclass)=4
END IF
ELSE IF (ts==5) THEN
which_irr(iclass)=5
ELSE
CALL errore('divide_class','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==3) THEN
which_irr(iclass)=2
ELSE IF (ts==4) THEN
which_irr(iclass)=3
ELSE IF (ts==2) THEN
which_irr(iclass)=4
ELSE IF (ts==6) THEN
which_irr(iclass)=5
ELSE IF (ts==5) THEN
which_irr(iclass)=6
ELSE
CALL errore('divide_class','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==4) THEN
which_irr(iclass)=3
ELSE IF (ts==6) THEN
IF (ABS(angle_rot_s(smat(1,1,elem(1,iclass)))-90.d0)<eps) THEN
which_irr(iclass)=2
ELSE
which_irr(iclass)=4
END IF
ELSE
CALL errore('divide_class','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==3) THEN
IF (ABS(angle_rot(smat(1,1,elem(1,iclass)))-120.d0)<eps) THEN
which_irr(iclass)=2
ELSE
which_irr(iclass)=3
END IF
ELSE IF (ts==2) THEN
which_irr(iclass)=4
ELSE IF (ts==6) THEN
IF (ABS(angle_rot_s(smat(1,1,elem(1,iclass)))-60.d0)<eps) THEN
which_irr(iclass)=6
ELSE
which_irr(iclass)=5
END IF
ELSE
CALL errore('divide_class','wrong operation',1)
END IF
END DO
ELSEIF (code_group==28) THEN
!
! T
!
DO iclass=2,nclass
ars=angle_rot(smat(1,1,elem(1,iclass)))
IF (ABS(ars-120.d0)<eps) THEN
which_irr(iclass)=2
ELSE IF (ABS(ars-240.d0)<eps) THEN
which_irr(iclass)=3
ELSE IF (ABS(ars-180.d0)<eps) THEN
which_irr(iclass)=4
ELSE
CALL errore('divide_class','wrong angle',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==3) THEN
IF (ABS(angle_rot(smat(1,1,elem(1,iclass)))-120.d0)<eps) THEN
which_irr(iclass)=2
ELSE
which_irr(iclass)=3
END IF
ELSE IF (ts==4) THEN
which_irr(iclass)=4
ELSE IF (ts==2) THEN
which_irr(iclass)=5
ELSE IF (ts==6) THEN
IF (ABS(angle_rot_s(smat(1,1,elem(1,iclass)))-60.d0)<eps) THEN
which_irr(iclass)=6
ELSE
which_irr(iclass)=7
END IF
ELSE IF (ts==5) THEN
which_irr(iclass)=8
ELSE
CALL errore('divide_class','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==3) THEN
which_irr(iclass)=2
ELSE IF (ts==4) THEN
which_irr(iclass)=3
ELSE IF (ts==6) THEN
which_irr(iclass)=4
ELSE IF (ts==5) THEN
which_irr(iclass)=5
ELSE
CALL errore('divide_class','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==4) THEN
IF (nelem(iclass)==3) THEN
which_irr(iclass)=3
ELSE
which_irr(iclass)=5
END IF
ELSE IF (ts==3) THEN
IF (nelem(iclass)==8) THEN
which_irr(iclass)=2
ELSE
which_irr(iclass)=4
END IF
ELSE
CALL errore('divide_class','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)==3) THEN
which_irr(iclass)=5
ELSE
which_irr(iclass)=3
END IF
ELSE IF (ts==3) THEN
IF (nelem(iclass)==8) THEN
which_irr(iclass)=2
ELSE
which_irr(iclass)=4
END IF
ELSE IF (ts==2) THEN
which_irr(iclass)=6
ELSE IF (ts==5) THEN
IF (nelem(iclass)==6) THEN
which_irr(iclass)=10
ELSE
which_irr(iclass)=9
END IF
ELSE IF (ts==6) THEN
IF (nelem(iclass)==8) THEN
which_irr(iclass)=8
ELSE
which_irr(iclass)=7
END IF
ELSE
CALL errore('divide_class_so','wrong operation',1)
END IF
ENDDO
ELSE
CALL errore('divide_class','code_group not correct',1)
ENDIF
RETURN
END SUBROUTINE divide_class
!-----------------------------------------------------------------------------
SUBROUTINE coniug_mat(a,b,c)
!-----------------------------------------------------------------------------
USE kinds, ONLY : DP
IMPLICIT NONE
REAL(DP) :: a(3,3), b(3,3), c(3,3)
c=MATMUL(a,MATMUL(b,TRANSPOSE(a)))
RETURN
END SUBROUTINE coniug_mat
!-----------------------------------------------------------------------------
FUNCTION compare_mat(a,b)
!-----------------------------------------------------------------------------
!
! This function compare two 3x3 matrix and returns .true. if they coincide.
!
USE kinds, ONLY : DP
IMPLICIT NONE
REAL(DP) :: a(3,3), b(3,3)
REAL(DP), PARAMETER :: eps=1.d-7
LOGICAL :: compare_mat
compare_mat=(ABS(MAXVAL(a-b))<eps).AND.(ABS(MINVAL(a-b))<eps)
END FUNCTION compare_mat
FUNCTION is_axis(ax,iflag)
!
! This is a logical function which returns .true. if ax is the versor
! of the axis x (iflag=1) or y (iflag=2) or z (iflag=3)
!
USE kinds, ONLY : DP
IMPLICIT NONE
REAL(DP) :: ax(3)
INTEGER :: iflag
LOGICAL :: is_axis
REAL(DP), PARAMETER :: eps=1.d-7
IF (iflag==1) THEN
is_axis=ABS(ax(2))<eps.AND.ABS(ax(3))<eps
ELSE IF (iflag==2) THEN
is_axis=ABS(ax(1))<eps.AND.ABS(ax(3))<eps
ELSE IF (iflag==3) THEN
is_axis=ABS(ax(1))<eps.AND.ABS(ax(2))<eps
ELSE
call errore('is_axis','iflag not allowed',1)
END IF
RETURN
END FUNCTION is_axis
!-----------------------------------------------------------------------------
SUBROUTINE versor(smat,ax)
!-----------------------------------------------------------------------------
!
! This subroutine receives a rotation matrix and determines the rotation
! axis. The orientation of the axis is with the tip in the hemisphere
! z>=0. In the xy plane the axis is in the y>0 region and the positive
! x axis is taken for z=0 and y=0.
!
USE kinds, ONLY : DP
IMPLICIT NONE
REAL(DP) :: smat(3,3), ax(3)
REAL(DP), PARAMETER :: eps=1.d-7
REAL(DP) :: a1(3), norm
INTEGER :: ipol, jpol, tipo_sym, ts
!
! Check if it is a 180 rotation
!
ts=tipo_sym(smat)
IF (ts/=3.and.ts/=4.and.ts/=6) &
call errore('versor','called in the wrong case',1)
IF (ts==4) THEN
!
! First the case where the axis is parallel to a coordinate axis
!
ax=0.d0
DO ipol=1,3
IF (ABS(smat(ipol,ipol)-1.d0) < eps ) ax(ipol)=1.d0
END DO
norm=sqrt(ax(1)**2+ax(2)**2+ax(3)**2)
IF (ABS(norm)>eps) RETURN
!
! then the general case
!
DO ipol=1,3
ax(ipol)=sqrt((smat(ipol,ipol)+1.d0)/2.d0)
END DO
DO ipol=1,3
DO jpol=ipol+1,3
IF (ABS(ax(ipol)*ax(jpol))>eps) THEN
ax(ipol)=0.5d0*smat(ipol,jpol)/ax(jpol)
END IF
END DO
END DO
RETURN
END IF
!
! It is not a 180 rotation: compute the rotation axis
!
a1(1) =-smat(2,3)+smat(3,2)
a1(2) =-smat(3,1)+smat(1,3)
a1(3) =-smat(1,2)+smat(2,1)
!
! The direction of the axis is arbitrarily chosen
!
IF (a1(3) < -eps ) THEN
a1=-a1
ELSEIF (abs(a1(3))<eps .and. a1(2) < -eps ) THEN
a1=-a1
ELSEIF (abs(a1(3))<eps .and. abs(a1(2))<eps.and.a1(1) < -eps ) THEN
a1=-a1
ENDIF
norm=sqrt(a1(1)**2+a1(2)**2+a1(3)**2)
IF (norm<eps) call errore('versor','problem with the matrix',1)
ax=a1/norm
RETURN
END SUBROUTINE versor
!-----------------------------------------------------------------------------
SUBROUTINE mirror_axis(smat,ax)
!-----------------------------------------------------------------------------
!
! This subroutine receives a mirror symmetry and determine the normal
! to the mirror plane. The sign of the normal is undefined.
!
USE kinds, ONLY : DP
IMPLICIT NONE
REAL(DP) :: smat(3,3), ax(3)
REAL(DP) :: aux_mat(3,3)
aux_mat=-smat
CALL versor(aux_mat,ax)
RETURN
END SUBROUTINE mirror_axis
!-----------------------------------------------------------------------------
FUNCTION angle_rot(smat)
!-----------------------------------------------------------------------------
!
! This subroutine receives a rotation matrix and determine the
! rotation angle.
!
USE kinds, ONLY : DP
IMPLICIT NONE
REAL(DP), PARAMETER :: eps=1.d-7
REAL(DP) :: smat(3,3)
REAL(DP) :: a1(3), ax(3)
REAL(DP) :: angle_rot, angle_rot1, pi, sint, cost
INTEGER :: tipo_sym
!
! Check if it is a 180 rotation
!
IF (tipo_sym(smat)==4) THEN
angle_rot=180.d0
RETURN
END IF
pi=4.d0*atan(1.d0)
!
! Compute the axis
!
a1(1) =-smat(2,3)+smat(3,2)
a1(2) =-smat(3,1)+smat(1,3)
a1(3) =-smat(1,2)+smat(2,1)
sint=0.5d0*sqrt(a1(1)**2+a1(2)**2+a1(3)**2)
IF (sint<eps) CALL errore('angle_rot','problem with the matrix',1)
!
! The direction of the axis is chosen in such a way that a1(3) is always
! positive if non zero. Otherwise a1(2) is positive, or a1(1) respectively
!
ax=a1
IF (ax(3) < -eps ) THEN
ax=-ax
ELSEIF (abs(ax(3))<eps .and. ax(2) < -eps ) THEN
ax=-ax
ELSEIF (abs(ax(3))<eps .and. abs(ax(2))<eps.and.ax(1) < -eps ) THEN
ax=-ax
ENDIF
IF (ABS(a1(1))>eps) THEN
sint=SIGN(sint,a1(1)/ax(1))
ELSEIF (ABS(a1(2))>eps) THEN
sint=SIGN(sint,a1(2)/ax(2))
ELSEIF (ABS(a1(3))>eps) THEN
sint=SIGN(sint,a1(3)/ax(3))
END IF
!
! Compute the cos of the angle
!
ax=a1/(2.d0*sint)
IF (ABS(ax(1)**2-1.d0)>eps) THEN
cost=(smat(1,1)-ax(1)**2)/(1.d0-ax(1)**2)
ELSE IF (ABS(ax(2)**2-1.d0)>eps) THEN
cost=(smat(2,2)-ax(2)**2)/(1.d0-ax(2)**2)
ELSE IF (ABS(ax(3)**2-1.d0)>eps) THEN
cost=(smat(3,3)-ax(3)**2)/(1.d0-ax(3)**2)
END IF
IF (ABS(sint**2+cost**2-1.d0) > eps ) &
CALL errore('angle_rot','problem with the matrix',1)
angle_rot1=ASIN(sint)*180.d0/pi
IF (angle_rot1 < 0.d0) THEN
IF (cost < 0.d0) THEN
angle_rot1=-angle_rot1+180.d0
ELSE
angle_rot1=360.d0+angle_rot1
ENDIF
ELSE
IF (cost < 0.d0) angle_rot1=-angle_rot1+180.d0
ENDIF
angle_rot=angle_rot1
RETURN
END FUNCTION angle_rot
!-----------------------------------------------------------------------------
FUNCTION angle_rot_s(smat)
!-----------------------------------------------------------------------------
!
! This subroutine receives an improper rotation matrix and determines the
! rotation angle.
!
USE kinds, ONLY : DP
IMPLICIT NONE
REAL(DP) :: smat(3,3)
REAL(DP) :: aux_mat(3,3)
REAL(DP) :: angle_rot, angle_rot_s
aux_mat=-smat
angle_rot_s=mod(angle_rot(aux_mat)+180.0_DP,360.0_DP)
RETURN
END FUNCTION angle_rot_s
!-----------------------------------------------------------------------------
SUBROUTINE set_irr_rap(code_group,nclass_ref,char_mat,name_rap, &
name_class,ir_ram)
!-----------------------------------------------------------------------------
!
! This subroutine collects the character tables of the 32 crystallographic
! point groups.
! Various names have been used in the litterature to identify
! the irreducible representations. Several equivalent names are
! collected in this routine. The first name is taken
! from the book of P.W. Atkins, M.S. Child, and C.S.G. Phillips,
! "Tables for group theory".
! D, G, L, S are used for Delta, Gamma, Lambda and Sigma.
! Representations which correspond to infrared or raman active modes
! are identified with the string in ir_ram: I (infrared active),
! R (Raman active), I+R (Infrared and Raman active).
!
!
USE kinds, ONLY : DP
IMPLICIT NONE
INTEGER :: nclass_ref, & ! Output: number of irreducible representation
code_group ! Input: code of the group
CHARACTER(LEN=15) :: name_rap(12) ! Output: name of the representations
CHARACTER(LEN=5) :: name_class(12) ! Output: name of the classes
CHARACTER(LEN=3) :: ir_ram(12)
COMPLEX(DP) :: char_mat(12,12) ! Output: character matrix
REAL(DP) :: sqr3d2
sqr3d2=SQRT(3.d0)*0.5d0
char_mat=(1.d0,0.d0)
name_class(1)="E "
ir_ram=" "
IF (code_group==1) THEN
!
! C_1
!
nclass_ref=1
name_rap(1)="A "
ir_ram(1)="I+R"
ELSEIF (code_group==2) THEN
!
! C_i
!
nclass_ref=2
name_class(2)="i "
name_rap(1)="A_g "
ir_ram(1)="R"
name_rap(2)="A_u "
ir_ram(2)="I"
char_mat(2,2)=(-1.d0,0.d0)
ELSEIF (code_group==3) THEN
!
! C_s
!
nclass_ref=2
name_class(2)="s "
name_rap(1)="A' "
ir_ram(1)="I+R"
name_rap(2)="A'' "
ir_ram(2)="I+R"
char_mat(2,2)=(-1.d0,0.d0)
ELSEIF (code_group==4) THEN
!
! C_2
!
nclass_ref=2
name_class(2)="C2 "
name_rap(1)="A "
ir_ram(1)="I+R"
name_rap(2)="B "
ir_ram(2)="I+R"
char_mat(2,2)=(-1.d0,0.d0)
ELSEIF (code_group==5) THEN
!
! C_3
!
nclass_ref=3
name_class(2)="C3 "
name_class(3)="C3^2 "
name_rap(1)="A "
ir_ram(1)="I+R"
name_rap(2)="E "
ir_ram(2)="I+R"
char_mat(2,2)=CMPLX(-0.5d0,sqr3d2)
char_mat(2,3)=CMPLX(-0.5d0,-sqr3d2)
name_rap(3)="E* "
ir_ram(3)="I+R"
char_mat(3,2)=CMPLX(-0.5d0,-sqr3d2)
char_mat(3,3)=CMPLX(-0.5d0,sqr3d2)
ELSEIF (code_group==6) THEN
!
! C_4
!
nclass_ref=4
name_class(2)="C4 "
name_class(3)="C2 "
name_class(4)="C4^3 "
name_rap(1)="A "
ir_ram(1)="I+R"
name_rap(2)="B "
ir_ram(2)="R"
char_mat(2,2)=(-1.d0,0.d0)
char_mat(2,4)=(-1.d0,0.d0)
name_rap(3)="E "
ir_ram(3)="I+R"
char_mat(3,2)=( 0.d0,1.d0)
char_mat(3,3)=(-1.d0,0.d0)
char_mat(3,4)=( 0.d0,-1.d0)
name_rap(4)="E* "
ir_ram(4)="I+R"
char_mat(4,2)=( 0.d0,-1.d0)
char_mat(4,3)=(-1.d0,0.d0)
char_mat(4,4)=( 0.d0,1.d0)
ELSEIF (code_group==7) THEN
!
! C_6
!
nclass_ref=6
name_class(2)="C6 "
name_class(3)="C3 "
name_class(4)="C2 "
name_class(5)="C3^2 "
name_class(6)="C6^5 "
name_rap(1)="A "
ir_ram(1)="I+R"
name_rap(2)="B "
char_mat(2,2)=(-1.d0,0.d0)
char_mat(2,4)=(-1.d0,0.d0)
char_mat(2,6)=(-1.d0,0.d0)
name_rap(3)="E_1 "
ir_ram(3)="I+R"
char_mat(3,2)=CMPLX( 0.5d0,sqr3d2)
char_mat(3,3)=CMPLX(-0.5d0,sqr3d2)
char_mat(3,4)=(-1.d0,0.d0)
char_mat(3,5)=CMPLX(-0.5d0,-sqr3d2)
char_mat(3,6)=CMPLX( 0.5d0,-sqr3d2)
name_rap(4)="E_1*"
ir_ram(4)="I+R"
char_mat(4,2)=CMPLX( 0.5d0,-sqr3d2)
char_mat(4,3)=CMPLX(-0.5d0,-sqr3d2)
char_mat(4,4)=(-1.d0,0.d0)
char_mat(4,5)=CMPLX(-0.5d0,sqr3d2)
char_mat(4,6)=CMPLX( 0.5d0,sqr3d2)
name_rap(5)="E_2 "
ir_ram(5)="R"
char_mat(5,2)=CMPLX(-0.5d0,sqr3d2)
char_mat(5,3)=CMPLX(-0.5d0,-sqr3d2)
char_mat(5,5)=CMPLX(-0.5d0,sqr3d2)
char_mat(5,6)=CMPLX(-0.5d0,-sqr3d2)
name_rap(6)="E_2*"
ir_ram(6)="R"
char_mat(6,2)=CMPLX(-0.5d0,-sqr3d2)
char_mat(6,3)=CMPLX(-0.5d0,sqr3d2)
char_mat(6,5)=CMPLX(-0.5d0,-sqr3d2)
char_mat(6,6)=CMPLX(-0.5d0,sqr3d2)
ELSEIF (code_group==8) THEN
!
! D_2
!
nclass_ref=4
name_class(2)="C2z "
name_class(3)="C2y "
name_class(4)="C2x "
name_rap(1)="A "
ir_ram(1)="R"
name_rap(2)="B_1 "
ir_ram(2)="I+R"
char_mat(2,3)=(-1.d0,0.d0)
char_mat(2,4)=(-1.d0,0.d0)
name_rap(3)="B_2 "
ir_ram(3)="I+R"
char_mat(3,2)=(-1.d0,0.d0)
char_mat(3,4)=(-1.d0,0.d0)
name_rap(4)="B_3 "
ir_ram(4)="I+R"
char_mat(4,2)=(-1.d0,0.d0)
char_mat(4,3)=(-1.d0,0.d0)
ELSEIF (code_group==9) THEN
!
! D_3
!
nclass_ref=3
name_class(2)="2C3 "
name_class(3)="3C2' "
name_rap(1)="A_1 "
ir_ram(1)="R"
name_rap(2)="A_2 "
ir_ram(2)="I"
char_mat(2,3)=(-1.d0,0.d0)
name_rap(3)="E "
ir_ram(3)="I+R"
char_mat(3,1)=( 2.d0,0.d0)
char_mat(3,2)=(-1.d0,0.d0)
char_mat(3,3)=( 0.d0,0.d0)
ELSEIF (code_group==10) THEN
!
! D_4
!
nclass_ref=5
name_class(2)="2C4 "
name_class(3)="C2 "
name_class(4)="2C2' "
name_class(5)="2C2''"
name_rap(1)="A_1 "
ir_ram(1)="R"
name_rap(2)="A_2 "
ir_ram(2)="I"
char_mat(2,4)=(-1.d0,0.d0)
char_mat(2,5)=(-1.d0,0.d0)
name_rap(3)="B_1 "
ir_ram(3)="R"
char_mat(3,2)=(-1.d0,0.d0)
char_mat(3,5)=(-1.d0,0.d0)
name_rap(4)="B_2 "
ir_ram(4)="R"
char_mat(4,2)=(-1.d0,0.d0)
char_mat(4,4)=(-1.d0,0.d0)
name_rap(5)="E "
ir_ram(5)="I+R"
char_mat(5,1)=( 2.d0,0.d0)
char_mat(5,2)=( 0.d0,0.d0)
char_mat(5,3)=(-2.d0,0.d0)
char_mat(5,4)=( 0.d0,0.d0)
char_mat(5,5)=( 0.d0,0.d0)
ELSEIF (code_group==11) THEN
!
! D_6
!
nclass_ref=6
name_class(2)="2C6 "
name_class(3)="2C3 "
name_class(4)="C2 "
name_class(5)="3C2' "
name_class(6)="3C2''"
name_rap(1)="A_1 "
ir_ram(1)="R"
name_rap(2)="A_2 "
ir_ram(2)="I"
char_mat(2,5)=(-1.d0,0.d0)
char_mat(2,6)=(-1.d0,0.d0)
name_rap(3)="B_1 "
char_mat(3,2)=(-1.d0,0.d0)
char_mat(3,4)=(-1.d0,0.d0)
char_mat(3,6)=(-1.d0,0.d0)
name_rap(4)="B_2 "
char_mat(4,2)=(-1.d0,0.d0)
char_mat(4,4)=(-1.d0,0.d0)
char_mat(4,5)=(-1.d0,0.d0)
name_rap(5)="E_1 "
ir_ram(5)="I+R"
char_mat(5,1)=( 2.d0,0.d0)
char_mat(5,3)=(-1.d0,0.d0)
char_mat(5,4)=(-2.d0,0.d0)
char_mat(5,5)=( 0.d0,0.d0)
char_mat(5,6)=( 0.d0,0.d0)
name_rap(6)="E_2 "
ir_ram(6)="R"
char_mat(6,1)=( 2.d0,0.d0)
char_mat(6,2)=(-1.d0,0.d0)
char_mat(6,3)=(-1.d0,0.d0)
char_mat(6,4)=( 2.d0,0.d0)
char_mat(6,5)=( 0.d0,0.d0)
char_mat(6,6)=( 0.d0,0.d0)
ELSEIF (code_group==12) THEN
!
! C_2v
!
nclass_ref=4
name_class(2)="C2 "
name_class(3)="s_xz "
name_class(4)="s_yz "
name_rap(1)="A_1 D_1 S_1"
ir_ram(1)="I+R"
name_rap(2)="A_2 D_2 S_2"
ir_ram(2)="R"
char_mat(2,3)=(-1.d0,0.d0)
char_mat(2,4)=(-1.d0,0.d0)
name_rap(3)="B_1 D_3 S_3"
ir_ram(3)="I+R"
char_mat(3,2)=(-1.d0,0.d0)
char_mat(3,4)=(-1.d0,0.d0)
name_rap(4)="B_2 D_4 S_4"
ir_ram(4)="I+R"
char_mat(4,2)=(-1.d0,0.d0)
char_mat(4,3)=(-1.d0,0.d0)
ELSEIF (code_group==13) THEN
!
! C_3v
!
nclass_ref=3
name_class(2)="2C3 "
name_class(3)="3s_v "
name_rap(1)="A_1 L_1"
ir_ram(1)="I+R"
name_rap(2)="A_2 L_2"
char_mat(2,3)=(-1.d0,0.d0)
name_rap(3)="E L_3"
ir_ram(3)="I+R"
char_mat(3,1)=( 2.d0,0.d0)
char_mat(3,2)=(-1.d0,0.d0)
char_mat(3,3)=( 0.d0,0.d0)
ELSEIF (code_group==14) THEN
!
! C_4v
!
nclass_ref=5
name_class(2)="2C4 "
name_class(3)="C2 "
name_class(4)="2s_v "
name_class(5)="2s_d "
name_rap(1)="A_1 G_1 D_1"
ir_ram(1)="I+R"
name_rap(2)="A_2 G_2 D_1'"
char_mat(2,4)=(-1.d0,0.d0)
char_mat(2,5)=(-1.d0,0.d0)
name_rap(3)="B_1 G_3 D_2"
ir_ram(3)="R"
char_mat(3,2)=(-1.d0,0.d0)
char_mat(3,5)=(-1.d0,0.d0)
name_rap(4)="B_2 G_4 D_2'"
ir_ram(4)="R"
char_mat(4,2)=(-1.d0,0.d0)
char_mat(4,4)=(-1.d0,0.d0)
name_rap(5)="E G_5 D_5"
ir_ram(5)="I+R"
char_mat(5,1)=( 2.d0,0.d0)
char_mat(5,2)=( 0.d0,0.d0)
char_mat(5,3)=(-2.d0,0.d0)
char_mat(5,4)=( 0.d0,0.d0)
char_mat(5,5)=( 0.d0,0.d0)
ELSEIF (code_group==15) THEN
!
! C_6v
!
nclass_ref=6
name_class(2)="2C6 "
name_class(3)="2C3 "
name_class(4)="C2 "
name_class(5)="3s_v "
name_class(6)="3s_d "
name_rap(1)="A_1 "
ir_ram(1)="I+R"
name_rap(2)="A_2 "
char_mat(2,5)=(-1.d0,0.d0)
char_mat(2,6)=(-1.d0,0.d0)
name_rap(3)="B_1 "
char_mat(3,2)=(-1.d0,0.d0)
char_mat(3,4)=(-1.d0,0.d0)
char_mat(3,6)=(-1.d0,0.d0)
name_rap(4)="B_2 "
char_mat(4,2)=(-1.d0,0.d0)
char_mat(4,4)=(-1.d0,0.d0)
char_mat(4,5)=(-1.d0,0.d0)
name_rap(5)="E_1 "
ir_ram(5)="I+R"
char_mat(5,1)=( 2.d0,0.d0)
char_mat(5,3)=(-1.d0,0.d0)
char_mat(5,4)=(-2.d0,0.d0)
char_mat(5,5)=( 0.d0,0.d0)
char_mat(5,6)=( 0.d0,0.d0)
name_rap(6)="E_2 "
ir_ram(6)="R"
char_mat(6,1)=( 2.d0,0.d0)
char_mat(6,2)=(-1.d0,0.d0)
char_mat(6,3)=(-1.d0,0.d0)
char_mat(6,4)=( 2.d0,0.d0)
char_mat(6,5)=( 0.d0,0.d0)
char_mat(6,6)=( 0.d0,0.d0)
ELSEIF (code_group==16) THEN
!
! C_2h
!
nclass_ref=4
name_class(2)="C2 "
name_class(3)="i "
name_class(4)="s_h "
name_rap(1)="A_g "
ir_ram(1)="R"
name_rap(2)="B_g "
ir_ram(2)="R"
char_mat(2,2)=(-1.d0,0.d0)
char_mat(2,4)=(-1.d0,0.d0)
name_rap(3)="A_u "
ir_ram(3)="I"
char_mat(3,3)=(-1.d0,0.d0)
char_mat(3,4)=(-1.d0,0.d0)
name_rap(4)="B_u "
ir_ram(4)="I"
char_mat(4,2)=(-1.d0,0.d0)
char_mat(4,3)=(-1.d0,0.d0)
ELSEIF (code_group==17) THEN
!
! C_3h
!
nclass_ref=6
name_class(2)="C3 "
name_class(3)="C3^2 "
name_class(4)="s_h "
name_class(5)="S3 "
name_class(6)="S3^5 "
name_rap(1)="A' "
ir_ram(1)="R"
name_rap(2)="E' "
ir_ram(2)="I+R"
char_mat(2,2)=CMPLX(-0.5d0,sqr3d2)
char_mat(2,3)=CMPLX(-0.5d0,-sqr3d2)
char_mat(2,5)=CMPLX(-0.5d0,sqr3d2)
char_mat(2,6)=CMPLX(-0.5d0,-sqr3d2)
name_rap(3)="E'* "
ir_ram(3)="I+R"
char_mat(3,2)=CMPLX(-0.5d0,-sqr3d2)
char_mat(3,3)=CMPLX(-0.5d0,sqr3d2)
char_mat(3,5)=CMPLX(-0.5d0,-sqr3d2)
char_mat(3,6)=CMPLX(-0.5d0,sqr3d2)
name_rap(4)="A'' "
ir_ram(4)="I"
char_mat(4,4)=(-1.d0,0.d0)
char_mat(4,5)=(-1.d0,0.d0)
char_mat(4,6)=(-1.d0,0.d0)
name_rap(5)="E'' "
ir_ram(5)="R"
char_mat(5,2)=CMPLX(-0.5d0,sqr3d2)
char_mat(5,3)=CMPLX(-0.5d0,-sqr3d2)
char_mat(5,4)=(-1.d0,0.d0)
char_mat(5,5)=CMPLX( 0.5d0,-sqr3d2)
char_mat(5,6)=CMPLX(0.5d0,sqr3d2)
name_rap(6)="E''*"
ir_ram(6)="R"
char_mat(6,2)=CMPLX(-0.5d0,-sqr3d2)
char_mat(6,3)=CMPLX(-0.5d0,sqr3d2)
char_mat(6,4)=(-1.d0,0.d0)
char_mat(6,5)=CMPLX( 0.5d0,sqr3d2)
char_mat(6,6)=CMPLX(0.5d0,-sqr3d2)
ELSEIF (code_group==18) THEN
!
! C_4h
!
nclass_ref=8
name_class(2)="C4 "
name_class(3)="C2 "
name_class(4)="C4^3 "
name_class(5)="i "
name_class(6)="S4^3 "
name_class(7)="s_h "
name_class(8)="S4 "
name_rap(1)="A_g "
ir_ram(1)="R"
name_rap(2)="B_g "
ir_ram(2)="R"
char_mat(2,2)=(-1.d0,0.d0)
char_mat(2,4)=(-1.d0,0.d0)
char_mat(2,6)=(-1.d0,0.d0)
char_mat(2,8)=(-1.d0,0.d0)
name_rap(3)="E_g "
ir_ram(3)="R"
char_mat(3,2)=( 0.d0,1.d0)
char_mat(3,3)=(-1.d0,0.d0)
char_mat(3,4)=( 0.d0,-1.d0)
char_mat(3,6)=( 0.d0,1.d0)
char_mat(3,7)=(-1.d0,0.d0)
char_mat(3,8)=( 0.d0,-1.d0)
name_rap(4)="E_g*"
ir_ram(4)="R"
char_mat(4,2)=(0.d0,-1.d0)
char_mat(4,3)=(-1.d0,0.d0)
char_mat(4,4)=( 0.d0,1.d0)
char_mat(4,6)=( 0.d0,-1.d0)
char_mat(4,7)=(-1.d0,0.d0)
char_mat(4,8)=( 0.d0,1.d0)
name_rap(5)="A_u "
ir_ram(5)="I"
char_mat(5,5)=(-1.d0,0.d0)
char_mat(5,6)=(-1.d0,0.d0)
char_mat(5,7)=(-1.d0,0.d0)
char_mat(5,8)=(-1.d0,0.d0)
name_rap(6)="B_u "
char_mat(6,2)=(-1.d0,0.d0)
char_mat(6,4)=(-1.d0,0.d0)
char_mat(6,5)=(-1.d0,0.d0)
char_mat(6,7)=(-1.d0,0.d0)
name_rap(7)="E_u "
ir_ram(7)="I"
char_mat(7,2)=( 0.d0,1.d0)
char_mat(7,3)=(-1.d0,0.d0)
char_mat(7,4)=( 0.d0,-1.d0)
char_mat(7,5)=(-1.d0, 0.d0)
char_mat(7,6)=( 0.d0,-1.d0)
char_mat(7,8)=( 0.d0,1.d0)
name_rap(8)="E_u*"
ir_ram(8)="I"
char_mat(8,2)=( 0.d0,-1.d0)
char_mat(8,3)=(-1.d0,0.d0)
char_mat(8,4)=( 0.d0,1.d0)
char_mat(8,5)=(-1.d0, 0.d0)
char_mat(8,6)=( 0.d0,1.d0)
char_mat(8,8)=( 0.d0,-1.d0)
ELSEIF (code_group==19) THEN
!
! C_6h
!
nclass_ref=12
name_class(2)="C6 "
name_class(3)="C3 "
name_class(4)="C2 "
name_class(5)="C3^2 "
name_class(6)="C6^5 "
name_class(7)="i "
name_class(8)="S3^5 "
name_class(9)="S6^5 "
name_class(10)="s_h "
name_class(11)="S6 "
name_class(12)="S3 "
name_rap(1)="A_g "
ir_ram(1)="R"
name_rap(2)="B_g "
char_mat(2,2)=(-1.d0,0.d0)
char_mat(2,4)=(-1.d0,0.d0)
char_mat(2,6)=(-1.d0,0.d0)
char_mat(2,8)=(-1.d0,0.d0)
char_mat(2,10)=(-1.d0,0.d0)
char_mat(2,12)=(-1.d0,0.d0)
name_rap(3)="E_1g"
ir_ram(3)="R"
char_mat(3,2)=CMPLX( 0.5d0, sqr3d2)
char_mat(3,3)=CMPLX(-0.5d0, sqr3d2)
char_mat(3,4)=(-1.d0,0.d0)
char_mat(3,5)=CMPLX(-0.5d0,-sqr3d2)
char_mat(3,6)=CMPLX( 0.5d0,-sqr3d2)
char_mat(3,8)=CMPLX( 0.5d0, sqr3d2)
char_mat(3,9)=CMPLX(-0.5d0, sqr3d2)
char_mat(3,10)=(-1.d0,0.d0)
char_mat(3,11)=CMPLX(-0.5d0,-sqr3d2)
char_mat(3,12)=CMPLX( 0.5d0,-sqr3d2)
name_rap(4)="E1g*"
ir_ram(4)="R"
char_mat(4,2)=CMPLX( 0.5d0,-sqr3d2)
char_mat(4,3)=CMPLX(-0.5d0,-sqr3d2)
char_mat(4,4)=(-1.d0,0.d0)
char_mat(4,5)=CMPLX(-0.5d0, sqr3d2)
char_mat(4,6)=CMPLX( 0.5d0, sqr3d2)
char_mat(4,8)=CMPLX( 0.5d0,-sqr3d2)
char_mat(4,9)=CMPLX(-0.5d0,-sqr3d2)
char_mat(4,10)=(-1.d0,0.d0)
char_mat(4,11)=CMPLX(-0.5d0,sqr3d2)
char_mat(4,12)=CMPLX( 0.5d0,sqr3d2)
name_rap(5)="E_2g"
ir_ram(5)="R"
char_mat(5,2)=CMPLX(-0.5d0, sqr3d2)
char_mat(5,3)=CMPLX(-0.5d0,-sqr3d2)
char_mat(5,5)=CMPLX(-0.5d0, sqr3d2)
char_mat(5,6)=CMPLX(-0.5d0,-sqr3d2)
char_mat(5,8)=CMPLX(-0.5d0, sqr3d2)
char_mat(5,9)=CMPLX(-0.5d0,-sqr3d2)
char_mat(5,11)=CMPLX(-0.5d0, sqr3d2)
char_mat(5,12)=CMPLX(-0.5d0,-sqr3d2)
name_rap(6)="E2g*"
ir_ram(6)="R"
char_mat(6,2)=CMPLX(-0.5d0,-sqr3d2)
char_mat(6,3)=CMPLX(-0.5d0, sqr3d2)
char_mat(6,5)=CMPLX(-0.5d0,-sqr3d2)
char_mat(6,6)=CMPLX(-0.5d0, sqr3d2)
char_mat(6,8)=CMPLX(-0.5d0,-sqr3d2)
char_mat(6,9)=CMPLX(-0.5d0, sqr3d2)
char_mat(6,11)=CMPLX(-0.5d0,-sqr3d2)
char_mat(6,12)=CMPLX(-0.5d0, sqr3d2)
name_rap(7)="A_u "
ir_ram(7)="I"
char_mat(7,7)=(-1.d0,0.d0)
char_mat(7,8)=(-1.d0,0.d0)
char_mat(7,9)=(-1.d0,0.d0)
char_mat(7,10)=(-1.d0,0.d0)
char_mat(7,11)=(-1.d0,0.d0)
char_mat(7,12)=(-1.d0,0.d0)
name_rap(8)="B_u "
char_mat(8,2)=(-1.d0,0.d0)
char_mat(8,4)=(-1.d0,0.d0)
char_mat(8,6)=(-1.d0,0.d0)
char_mat(8,7)=(-1.d0,0.d0)
char_mat(8,9)=(-1.d0,0.d0)
char_mat(8,11)=(-1.d0,0.d0)
name_rap(9)="E_1u"
ir_ram(9)="I"
char_mat(9,2)=CMPLX( 0.5d0, sqr3d2)
char_mat(9,3)=CMPLX(-0.5d0, sqr3d2)
char_mat(9,4)=(-1.d0,0.d0)
char_mat(9,5)=CMPLX(-0.5d0,-sqr3d2)
char_mat(9,6)=CMPLX( 0.5d0,-sqr3d2)
char_mat(9,7)=(-1.d0,0.d0)
char_mat(9,8)=CMPLX(-0.5d0,-sqr3d2)
char_mat(9,9)=CMPLX( 0.5d0,-sqr3d2)
char_mat(9,11)=CMPLX( 0.5d0, sqr3d2)
char_mat(9,12)=CMPLX(-0.5d0, sqr3d2)
name_rap(10)="E1u*"
ir_ram(10)="I"
char_mat(10,2)=CMPLX( 0.5d0,-sqr3d2)
char_mat(10,3)=CMPLX(-0.5d0,-sqr3d2)
char_mat(10,4)=(-1.d0,0.d0)
char_mat(10,5)=CMPLX(-0.5d0, sqr3d2)
char_mat(10,6)=CMPLX( 0.5d0, sqr3d2)
char_mat(10,7)=(-1.d0,0.d0)
char_mat(10,8)=CMPLX(-0.5d0, sqr3d2)
char_mat(10,9)=CMPLX( 0.5d0, sqr3d2)
char_mat(10,11)=CMPLX( 0.5d0,-sqr3d2)
char_mat(10,12)=CMPLX(-0.5d0,-sqr3d2)
name_rap(11)="E_2u"
char_mat(11,2)=CMPLX(-0.5d0, sqr3d2)
char_mat(11,3)=CMPLX(-0.5d0,-sqr3d2)
char_mat(11,5)=CMPLX(-0.5d0, sqr3d2)
char_mat(11,6)=CMPLX(-0.5d0,-sqr3d2)
char_mat(11,7)=(-1.d0,0.d0)
char_mat(11,8)=CMPLX( 0.5d0,-sqr3d2)
char_mat(11,9)=CMPLX( 0.5d0, sqr3d2)
char_mat(11,10)=(-1.d0,0.d0)
char_mat(11,11)=CMPLX( 0.5d0,-sqr3d2)
char_mat(11,12)=CMPLX( 0.5d0, sqr3d2)
name_rap(12)="E2u*"
char_mat(12,2)=CMPLX(-0.5d0,-sqr3d2)
char_mat(12,3)=CMPLX(-0.5d0, sqr3d2)
char_mat(12,5)=CMPLX(-0.5d0,-sqr3d2)
char_mat(12,6)=CMPLX(-0.5d0, sqr3d2)
char_mat(12,7)=(-1.d0,0.d0)
char_mat(12,8)=CMPLX( 0.5d0, sqr3d2)
char_mat(12,9)=CMPLX( 0.5d0,-sqr3d2)
char_mat(12,10)=(-1.d0,0.d0)
char_mat(12,11)=CMPLX( 0.5d0, sqr3d2)
char_mat(12,12)=CMPLX( 0.5d0,-sqr3d2)
ELSEIF (code_group==20) THEN
!
! D_2h
!
nclass_ref=8
name_class(2)="C2_z "
name_class(3)="C2_y "
name_class(4)="C2_x "
name_class(5)="i "
name_class(6)="s_xy "
name_class(7)="s_xz "
name_class(8)="s_yz "
name_rap(1)="A_g "
ir_ram(1)="R"
name_rap(2)="B_1g"
ir_ram(2)="R"
char_mat(2,3)=(-1.d0,0.d0)
char_mat(2,4)=(-1.d0,0.d0)
char_mat(2,7)=(-1.d0,0.d0)
char_mat(2,8)=(-1.d0,0.d0)
name_rap(3)="B_2g"
ir_ram(3)="R"
char_mat(3,2)=(-1.d0,0.d0)
char_mat(3,4)=(-1.d0,0.d0)
char_mat(3,6)=(-1.d0,0.d0)
char_mat(3,8)=(-1.d0,0.d0)
name_rap(4)="B_3g"
ir_ram(4)="R"
char_mat(4,2)=(-1.d0,0.d0)
char_mat(4,3)=(-1.d0,0.d0)
char_mat(4,6)=(-1.d0,0.d0)
char_mat(4,7)=(-1.d0,0.d0)
name_rap(5)="A_u "
char_mat(5,5)=(-1.d0,0.d0)
char_mat(5,6)=(-1.d0,0.d0)
char_mat(5,7)=(-1.d0,0.d0)
char_mat(5,8)=(-1.d0,0.d0)
name_rap(6)="B_1u"
ir_ram(6)="I"
char_mat(6,3)=(-1.d0,0.d0)
char_mat(6,4)=(-1.d0,0.d0)
char_mat(6,5)=(-1.d0,0.d0)
char_mat(6,6)=(-1.d0,0.d0)
name_rap(7)="B_2u"
ir_ram(7)="I"
char_mat(7,2)=(-1.d0,0.d0)
char_mat(7,4)=(-1.d0,0.d0)
char_mat(7,5)=(-1.d0,0.d0)
char_mat(7,7)=(-1.d0,0.d0)
name_rap(8)="B_3u"
ir_ram(8)="I"
char_mat(8,2)=(-1.d0,0.d0)
char_mat(8,3)=(-1.d0,0.d0)
char_mat(8,5)=(-1.d0,0.d0)
char_mat(8,8)=(-1.d0,0.d0)
ELSEIF (code_group==21) THEN
!
! D_3h
!
nclass_ref=6
name_class(2)="2C3 "
name_class(3)="3C2 "
name_class(4)="s_h "
name_class(5)="2S3 "
name_class(6)="3s_v "
name_rap(1)="A'_1"
ir_ram(1)="R"
name_rap(2)="A'_2"
char_mat(2,3)=(-1.d0,0.d0)
char_mat(2,6)=(-1.d0,0.d0)
name_rap(3)="E' "
ir_ram(3)="I+R"
char_mat(3,1)=( 2.d0,0.d0)
char_mat(3,2)=(-1.d0,0.d0)
char_mat(3,3)=( 0.d0,0.d0)
char_mat(3,4)=( 2.d0,0.d0)
char_mat(3,5)=(-1.d0,0.d0)
char_mat(3,6)=( 0.d0,0.d0)
name_rap(4)="A''1"
char_mat(4,4)=(-1.d0,0.d0)
char_mat(4,5)=(-1.d0,0.d0)
char_mat(4,6)=(-1.d0,0.d0)
name_rap(5)="A''2"
ir_ram(5)="I"
char_mat(5,3)=(-1.d0,0.d0)
char_mat(5,4)=(-1.d0,0.d0)
char_mat(5,5)=(-1.d0,0.d0)
name_rap(6)="E'' "
ir_ram(6)="R"
char_mat(6,1)=( 2.d0,0.d0)
char_mat(6,2)=(-1.d0,0.d0)
char_mat(6,3)=( 0.d0,0.d0)
char_mat(6,4)=(-2.d0,0.d0)
char_mat(6,6)=( 0.d0,0.d0)
ELSEIF (code_group==22) THEN
!
! D_4h
!
nclass_ref=10
name_class(2)="2C4 "
name_class(3)="C2 "
name_class(4)="2C2' "
name_class(5)="2C2''"
name_class(6)="i "
name_class(7)="2S4 "
name_class(8)="s_h "
name_class(9)="2s_v "
name_class(10)="2s_d "
name_rap(1)="A_1g X_1 M_1"
ir_ram(1)="R"
name_rap(2)="A_2g X_4 M_4"
char_mat(2,4)=(-1.d0,0.d0)
char_mat(2,5)=(-1.d0,0.d0)
char_mat(2,9)=(-1.d0,0.d0)
char_mat(2,10)=(-1.d0,0.d0)
name_rap(3)="B_1g X_2 M_2"
ir_ram(3)="R"
char_mat(3,2)=(-1.d0,0.d0)
char_mat(3,5)=(-1.d0,0.d0)
char_mat(3,7)=(-1.d0,0.d0)
char_mat(3,10)=(-1.d0,0.d0)
name_rap(4)="B_2g X_3 M_3"
ir_ram(4)="R"
char_mat(4,2)=(-1.d0,0.d0)
char_mat(4,4)=(-1.d0,0.d0)
char_mat(4,7)=(-1.d0,0.d0)
char_mat(4,9)=(-1.d0,0.d0)
name_rap(5)="E_g X_5 M_5"
ir_ram(5)="R"
char_mat(5,1)=( 2.d0,0.d0)
char_mat(5,2)=( 0.d0,0.d0)
char_mat(5,3)=(-2.d0,0.d0)
char_mat(5,4)=( 0.d0,0.d0)
char_mat(5,5)=( 0.d0,0.d0)
char_mat(5,6)=( 2.d0,0.d0)
char_mat(5,7)=( 0.d0,0.d0)
char_mat(5,8)=(-2.d0,0.d0)
char_mat(5,9)=( 0.d0,0.d0)
char_mat(5,10)=( 0.d0,0.d0)
name_rap(6)="A_1u X_1' M_1'"
char_mat(6,6)=(-1.d0,0.d0)
char_mat(6,7)=(-1.d0,0.d0)
char_mat(6,8)=(-1.d0,0.d0)
char_mat(6,9)=(-1.d0,0.d0)
char_mat(6,10)=(-1.d0,0.d0)
name_rap(7)="A_2u X_4' M_4'"
ir_ram(7)="I"
char_mat(7,4)=(-1.d0,0.d0)
char_mat(7,5)=(-1.d0,0.d0)
char_mat(7,6)=(-1.d0,0.d0)
char_mat(7,7)=(-1.d0,0.d0)
char_mat(7,8)=(-1.d0,0.d0)
name_rap(8)="B_1u X_2' M_2'"
char_mat(8,2)=(-1.d0,0.d0)
char_mat(8,5)=(-1.d0,0.d0)
char_mat(8,6)=(-1.d0,0.d0)
char_mat(8,8)=(-1.d0,0.d0)
char_mat(8,9)=(-1.d0,0.d0)
name_rap(9)="B_2u X_3' M_3'"
char_mat(9,2)=(-1.d0,0.d0)
char_mat(9,4)=(-1.d0,0.d0)
char_mat(9,6)=(-1.d0,0.d0)
char_mat(9,8)=(-1.d0,0.d0)
char_mat(9,10)=(-1.d0,0.d0)
name_rap(10)="E_u X_5' M_5'"
ir_ram(10)="I"
char_mat(10,1)=( 2.d0,0.d0)
char_mat(10,2)=( 0.d0,0.d0)
char_mat(10,3)=(-2.d0,0.d0)
char_mat(10,4)=( 0.d0,0.d0)
char_mat(10,5)=( 0.d0,0.d0)
char_mat(10,6)=(-2.d0,0.d0)
char_mat(10,7)=( 0.d0,0.d0)
char_mat(10,8)=( 2.d0,0.d0)
char_mat(10,9)=( 0.d0,0.d0)
char_mat(10,10)=( 0.d0,0.d0)
ELSEIF (code_group==23) THEN
!
! D_6h
!
nclass_ref=12
name_class(2)="2C6 "
name_class(3)="2C3 "
name_class(4)="C2 "
name_class(5)="3C2' "
name_class(6)="3C2''"
name_class(7)="i "
name_class(8)="2S3 "
name_class(9)="2S6 "
name_class(10)="s_h "
name_class(11)="3s_d "
name_class(12)="3s_v "
name_rap(1)="A_1g"
ir_ram(1)="R"
name_rap(2)="A_2g"
char_mat(2,5)=(-1.d0,0.d0)
char_mat(2,6)=(-1.d0,0.d0)
char_mat(2,11)=(-1.d0,0.d0)
char_mat(2,12)=(-1.d0,0.d0)
name_rap(3)="B_1g"
char_mat(3,2)=(-1.d0,0.d0)
char_mat(3,4)=(-1.d0,0.d0)
char_mat(3,6)=(-1.d0,0.d0)
char_mat(3,8)=(-1.d0,0.d0)
char_mat(3,10)=(-1.d0,0.d0)
char_mat(3,12)=(-1.d0,0.d0)
name_rap(4)="B_2g"
char_mat(4,2)=(-1.d0,0.d0)
char_mat(4,4)=(-1.d0,0.d0)
char_mat(4,5)=(-1.d0,0.d0)
char_mat(4,8)=(-1.d0,0.d0)
char_mat(4,10)=(-1.d0,0.d0)
char_mat(4,11)=(-1.d0,0.d0)
name_rap(5)="E_1g"
ir_ram(5)="R"
char_mat(5,1)=( 2.d0,0.d0)
char_mat(5,3)=(-1.d0,0.d0)
char_mat(5,4)=(-2.d0,0.d0)
char_mat(5,5)=( 0.d0,0.d0)
char_mat(5,6)=( 0.d0,0.d0)
char_mat(5,7)=( 2.d0,0.d0)
char_mat(5,9)=(-1.d0,0.d0)
char_mat(5,10)=(-2.d0,0.d0)
char_mat(5,11)=( 0.d0,0.d0)
char_mat(5,12)=( 0.d0,0.d0)
name_rap(6)="E_2g"
ir_ram(6)="R"
char_mat(6,1)=( 2.d0,0.d0)
char_mat(6,2)=(-1.d0,0.d0)
char_mat(6,3)=(-1.d0,0.d0)
char_mat(6,4)=( 2.d0,0.d0)
char_mat(6,5)=( 0.d0,0.d0)
char_mat(6,6)=( 0.d0,0.d0)
char_mat(6,7)=( 2.d0,0.d0)
char_mat(6,8)=(-1.d0,0.d0)
char_mat(6,9)=(-1.d0,0.d0)
char_mat(6,10)=( 2.d0,0.d0)
char_mat(6,11)=( 0.d0,0.d0)
char_mat(6,12)=( 0.d0,0.d0)
name_rap(7)="A_1u"
char_mat(7,7)=(-1.d0,0.d0)
char_mat(7,8)=(-1.d0,0.d0)
char_mat(7,9)=(-1.d0,0.d0)
char_mat(7,10)=(-1.d0,0.d0)
char_mat(7,11)=(-1.d0,0.d0)
char_mat(7,12)=(-1.d0,0.d0)
name_rap(8)="A_2u"
ir_ram(8)="I"
char_mat(8,5)=(-1.d0,0.d0)
char_mat(8,6)=(-1.d0,0.d0)
char_mat(8,7)=(-1.d0,0.d0)
char_mat(8,8)=(-1.d0,0.d0)
char_mat(8,9)=(-1.d0,0.d0)
char_mat(8,10)=(-1.d0,0.d0)
name_rap(9)="B_1u"
char_mat(9,2)=(-1.d0,0.d0)
char_mat(9,4)=(-1.d0,0.d0)
char_mat(9,6)=(-1.d0,0.d0)
char_mat(9,7)=(-1.d0,0.d0)
char_mat(9,9)=(-1.d0,0.d0)
char_mat(9,11)=(-1.d0,0.d0)
name_rap(10)="B_2u"
char_mat(10,2)=(-1.d0,0.d0)
char_mat(10,4)=(-1.d0,0.d0)
char_mat(10,5)=(-1.d0,0.d0)
char_mat(10,7)=(-1.d0,0.d0)
char_mat(10,9)=(-1.d0,0.d0)
char_mat(10,12)=(-1.d0,0.d0)
name_rap(11)="E_1u"
ir_ram(11)="I"
char_mat(11,1)=( 2.d0,0.d0)
char_mat(11,3)=(-1.d0,0.d0)
char_mat(11,4)=(-2.d0,0.d0)
char_mat(11,5)=( 0.d0,0.d0)
char_mat(11,6)=( 0.d0,0.d0)
char_mat(11,7)=(-2.d0,0.d0)
char_mat(11,8)=(-1.d0,0.d0)
char_mat(11,10)=( 2.d0,0.d0)
char_mat(11,11)=( 0.d0,0.d0)
char_mat(11,12)=( 0.d0,0.d0)
name_rap(12)="E_2u"
char_mat(12,1)=( 2.d0,0.d0)
char_mat(12,2)=(-1.d0,0.d0)
char_mat(12,3)=(-1.d0,0.d0)
char_mat(12,4)=( 2.d0,0.d0)
char_mat(12,5)=( 0.d0,0.d0)
char_mat(12,6)=( 0.d0,0.d0)
char_mat(12,7)=(-2.d0,0.d0)
char_mat(12,10)=(-2.d0,0.d0)
char_mat(12,11)=( 0.d0,0.d0)
char_mat(12,12)=( 0.d0,0.d0)
ELSEIF (code_group==24) THEN
!
! D_2d
!
nclass_ref=5
name_class(2)="2S4 "
name_class(3)="C2 "
name_class(4)="2C2' "
name_class(5)="2s_d "
name_rap(1)="A_1 X_1 W_1"
ir_ram(1)="R"
name_rap(2)="A_2 X_4 W_2'"
char_mat(2,4)=(-1.d0,0.d0)
char_mat(2,5)=(-1.d0,0.d0)
name_rap(3)="B_1 X_2 W_1'"
ir_ram(3)="R"
char_mat(3,2)=(-1.d0,0.d0)
char_mat(3,5)=(-1.d0,0.d0)
name_rap(4)="B_2 X_3 W_2"
ir_ram(4)="I+R"
char_mat(4,2)=(-1.d0,0.d0)
char_mat(4,4)=(-1.d0,0.d0)
name_rap(5)="E X_5 W_3"
ir_ram(5)="I+R"
char_mat(5,1)=( 2.d0,0.d0)
char_mat(5,2)=( 0.d0,0.d0)
char_mat(5,3)=(-2.d0,0.d0)
char_mat(5,4)=( 0.d0,0.d0)
char_mat(5,5)=( 0.d0,0.d0)
ELSEIF (code_group==25) THEN
!
! D_3d
!
nclass_ref=6
name_class(2)="2C3 "
name_class(3)="3C2' "
name_class(4)="i "
name_class(5)="2S6 "
name_class(6)="3s_d "
name_rap(1)="A_1g L_1"
ir_ram(1)="R"
name_rap(2)="A_2g L_2"
char_mat(2,3)=(-1.d0,0.d0)
char_mat(2,6)=(-1.d0,0.d0)
name_rap(3)="E_g L_3"
ir_ram(3)="R"
char_mat(3,1)=( 2.d0,0.d0)
char_mat(3,2)=(-1.d0,0.d0)
char_mat(3,3)=( 0.d0,0.d0)
char_mat(3,4)=( 2.d0,0.d0)
char_mat(3,5)=(-1.d0,0.d0)
char_mat(3,6)=( 0.d0,0.d0)
name_rap(4)="A_1u L_1'"
char_mat(4,4)=(-1.d0,0.d0)
char_mat(4,5)=(-1.d0,0.d0)
char_mat(4,6)=(-1.d0,0.d0)
name_rap(5)="A_2u L_2'"
ir_ram(5)="I"
char_mat(5,3)=(-1.d0,0.d0)
char_mat(5,4)=(-1.d0,0.d0)
char_mat(5,5)=(-1.d0,0.d0)
name_rap(6)="E_u L_3'"
ir_ram(6)="I"
char_mat(6,1)=( 2.d0,0.d0)
char_mat(6,2)=(-1.d0,0.d0)
char_mat(6,3)=( 0.d0,0.d0)
char_mat(6,4)=(-2.d0,0.d0)
char_mat(6,6)=( 0.d0,0.d0)
ELSEIF (code_group==26) THEN
!
! S_4
!
nclass_ref=4
name_class(2)="S4 "
name_class(3)="C2 "
name_class(4)="S4^3 "
name_rap(1)="A W_1"
ir_ram(1)="R"
name_rap(2)="B W_3"
ir_ram(2)="I+R"
char_mat(2,2)=(-1.d0,0.d0)
char_mat(2,4)=(-1.d0,0.d0)
name_rap(3)="E W_4"
ir_ram(3)="I+R"
char_mat(3,2)=( 0.d0, 1.d0)
char_mat(3,3)=(-1.d0,0.d0)
char_mat(3,4)=( 0.d0,-1.d0)
name_rap(4)="E* W_2"
ir_ram(4)="I+R"
char_mat(4,2)=( 0.d0,-1.d0)
char_mat(4,3)=(-1.d0,0.d0)
char_mat(4,4)=( 0.d0, 1.d0)
ELSEIF (code_group==27) THEN
!
! S_6
!
nclass_ref=6
name_class(2)="C3 "
name_class(3)="C3^2 "
name_class(4)="i "
name_class(5)="S6^5 "
name_class(6)="S6 "
name_rap(1)="A_g "
ir_ram(1)="R"
name_rap(2)="E_g "
ir_ram(2)="R"
char_mat(2,2)=CMPLX(-0.5d0,sqr3d2)
char_mat(2,3)=CMPLX(-0.5d0,-sqr3d2)
char_mat(2,5)=CMPLX(-0.5d0,sqr3d2)
char_mat(2,6)=CMPLX(-0.5d0,-sqr3d2)
name_rap(3)="E_g*"
ir_ram(3)="R"
char_mat(3,2)=CMPLX(-0.5d0,-sqr3d2)
char_mat(3,3)=CMPLX(-0.5d0,sqr3d2)
char_mat(3,5)=CMPLX(-0.5d0,-sqr3d2)
char_mat(3,6)=CMPLX(-0.5d0,sqr3d2)
name_rap(4)="A_u "
ir_ram(4)="I"
char_mat(4,4)=(-1.d0,0.d0)
char_mat(4,5)=(-1.d0,0.d0)
char_mat(4,6)=(-1.d0,0.d0)
name_rap(5)="E_u "
ir_ram(5)="I"
char_mat(5,2)=CMPLX(-0.5d0,sqr3d2)
char_mat(5,3)=CMPLX(-0.5d0,-sqr3d2)
char_mat(5,4)=(-1.d0,0.d0)
char_mat(5,5)=CMPLX( 0.5d0,-sqr3d2)
char_mat(5,6)=CMPLX( 0.5d0, sqr3d2)
name_rap(6)="E_u*"
ir_ram(6)="I"
char_mat(6,2)=CMPLX(-0.5d0,-sqr3d2)
char_mat(6,3)=CMPLX(-0.5d0,sqr3d2)
char_mat(6,4)=(-1.d0,0.d0)
char_mat(6,5)=CMPLX( 0.5d0,sqr3d2)
char_mat(6,6)=CMPLX( 0.5d0,-sqr3d2)
ELSEIF (code_group==28) THEN
!
! T
!
nclass_ref=4
name_class(2)="4C3 "
name_class(3)="4C3' "
name_class(4)="3C2 "
name_rap(1)="A "
ir_ram(1)="R"
name_rap(2)="E "
ir_ram(2)="R"
char_mat(2,2)=CMPLX(-0.5d0, sqr3d2)
char_mat(2,3)=CMPLX(-0.5d0,-sqr3d2)
name_rap(3)="E* "
ir_ram(3)="R"
char_mat(3,2)=CMPLX(-0.5d0,-sqr3d2)
char_mat(3,3)=CMPLX(-0.5d0, sqr3d2)
name_rap(4)="T "
ir_ram(4)="I+R"
char_mat(4,1)=( 3.0d0,0.d0)
char_mat(4,2)=( 0.0d0,0.d0)
char_mat(4,3)=( 0.0d0,0.d0)
char_mat(4,4)=(-1.0d0,0.d0)
ELSEIF (code_group==29) THEN
!
! T_h
!
nclass_ref=8
name_class(2)="4C3 "
name_class(3)="4C3' "
name_class(4)="3C2 "
name_class(5)="i "
name_class(6)="4S6 "
name_class(7)="4S6^5"
name_class(8)="3s_h "
name_rap(1)="A_g "
ir_ram(1)="R"
name_rap(2)="E_g "
ir_ram(2)="R"
char_mat(2,2)=CMPLX(-0.5d0, sqr3d2)
char_mat(2,3)=CMPLX(-0.5d0,-sqr3d2)
char_mat(2,6)=CMPLX(-0.5d0, sqr3d2)
char_mat(2,7)=CMPLX(-0.5d0,-sqr3d2)
name_rap(3)="E_g*"
ir_ram(3)="R"
char_mat(3,2)=CMPLX(-0.5d0,-sqr3d2)
char_mat(3,3)=CMPLX(-0.5d0, sqr3d2)
char_mat(3,6)=CMPLX(-0.5d0,-sqr3d2)
char_mat(3,7)=CMPLX(-0.5d0, sqr3d2)
name_rap(4)="T_g "
ir_ram(4)="R"
char_mat(4,1)=( 3.0d0,0.d0)
char_mat(4,2)=( 0.0d0,0.d0)
char_mat(4,3)=( 0.0d0,0.d0)
char_mat(4,4)=(-1.0d0,0.d0)
char_mat(4,5)=( 3.0d0,0.d0)
char_mat(4,6)=( 0.0d0,0.d0)
char_mat(4,7)=( 0.0d0,0.d0)
char_mat(4,8)=(-1.0d0,0.d0)
name_rap(5)="A_u "
char_mat(5,5)=(-1.0d0,0.d0)
char_mat(5,6)=(-1.0d0,0.d0)
char_mat(5,7)=(-1.0d0,0.d0)
char_mat(5,8)=(-1.0d0,0.d0)
name_rap(6)="E_u "
char_mat(6,2)=CMPLX(-0.5d0, sqr3d2)
char_mat(6,3)=CMPLX(-0.5d0,-sqr3d2)
char_mat(6,5)=(-1.0d0,0.d0)
char_mat(6,6)=CMPLX( 0.5d0,-sqr3d2)
char_mat(6,7)=CMPLX( 0.5d0, sqr3d2)
char_mat(6,8)=(-1.0d0,0.d0)
name_rap(7)="E_u*"
char_mat(7,2)=CMPLX(-0.5d0,-sqr3d2)
char_mat(7,3)=CMPLX(-0.5d0, sqr3d2)
char_mat(7,5)=(-1.0d0,0.d0)
char_mat(7,6)=CMPLX( 0.5d0, sqr3d2)
char_mat(7,7)=CMPLX( 0.5d0,-sqr3d2)
char_mat(7,8)=(-1.0d0,0.d0)
name_rap(8)="T_u "
ir_ram(8)="I"
char_mat(8,1)=( 3.0d0,0.d0)
char_mat(8,2)=( 0.0d0,0.d0)
char_mat(8,3)=( 0.0d0,0.d0)
char_mat(8,4)=(-1.0d0,0.d0)
char_mat(8,5)=(-3.0d0,0.d0)
char_mat(8,6)=( 0.0d0,0.d0)
char_mat(8,7)=( 0.0d0,0.d0)
ELSEIF (code_group==30) THEN
!
! T_d
!
nclass_ref=5
name_class(2)="8C3 "
name_class(3)="3C2 "
name_class(4)="6S4 "
name_class(5)="6s_d "
name_rap(1)="A_1 G_1 P_1"
ir_ram(1)="R"
name_rap(2)="A_2 G_2 P_2"
char_mat(2,4)=(-1.d0,0.d0)
char_mat(2,5)=(-1.d0,0.d0)
name_rap(3)="E G_12 P_3"
ir_ram(3)="R"
char_mat(3,1)=( 2.d0,0.d0)
char_mat(3,2)=(-1.d0,0.d0)
char_mat(3,3)=( 2.d0,0.d0)
char_mat(3,4)=( 0.d0,0.d0)
char_mat(3,5)=( 0.d0,0.d0)
name_rap(4)="T_1 G_25 P_5"
char_mat(4,1)=( 3.d0,0.d0)
char_mat(4,2)=( 0.d0,0.d0)
char_mat(4,3)=(-1.d0,0.d0)
char_mat(4,5)=(-1.d0,0.d0)
name_rap(5)="T_2 G_15 P_4"
ir_ram(5)="I+R"
char_mat(5,1)=( 3.d0,0.d0)
char_mat(5,2)=( 0.d0,0.d0)
char_mat(5,3)=(-1.d0,0.d0)
char_mat(5,4)=(-1.d0,0.d0)
ELSEIF (code_group==31) THEN
!
! O
!
nclass_ref=5
name_class(2)="8C3 "
name_class(3)="3C2 "
name_class(4)="6C2 "
name_class(5)="6C4 "
name_rap(1)="A_1 "
ir_ram(1)="R"
name_rap(2)="A_2 "
char_mat(2,4)=(-1.d0,0.d0)
char_mat(2,5)=(-1.d0,0.d0)
name_rap(3)="E "
ir_ram(3)="R"
char_mat(3,1)=( 2.d0,0.d0)
char_mat(3,2)=(-1.d0,0.d0)
char_mat(3,3)=( 2.d0,0.d0)
char_mat(3,4)=( 0.d0,0.d0)
char_mat(3,5)=( 0.d0,0.d0)
name_rap(4)="T_1 "
ir_ram(4)="I"
char_mat(4,1)=( 3.d0,0.d0)
char_mat(4,2)=( 0.d0,0.d0)
char_mat(4,3)=(-1.d0,0.d0)
char_mat(4,5)=(-1.d0,0.d0)
name_rap(5)="T_2 "
ir_ram(5)="R"
char_mat(5,1)=( 3.d0,0.d0)
char_mat(5,2)=( 0.d0,0.d0)
char_mat(5,3)=(-1.d0,0.d0)
char_mat(5,4)=(-1.d0,0.d0)
ELSEIF (code_group==32) THEN
!
! O_h
!
nclass_ref=10
name_class(2)="8C3 "
name_class(3)="6C2' "
name_class(4)="6C4 "
name_class(5)="3C2 "
name_class(6)="i "
name_class(7)="6S4 "
name_class(8)="8S6 "
name_class(9)="3s_h "
name_class(10)="6s_d "
name_rap(1)="A_1g G_1 G_1+"
ir_ram(1)="R"
name_rap(2)="A_2g G_2 G_2+"
char_mat(2,3)=(-1.d0,0.d0)
char_mat(2,4)=(-1.d0,0.d0)
char_mat(2,7)=(-1.d0,0.d0)
char_mat(2,10)=(-1.d0,0.d0)
name_rap(3)="E_g G_12 G_3+"
ir_ram(3)="R"
char_mat(3,1)=( 2.d0,0.d0)
char_mat(3,2)=(-1.d0,0.d0)
char_mat(3,3)=( 0.d0,0.d0)
char_mat(3,4)=( 0.d0,0.d0)
char_mat(3,5)=( 2.d0,0.d0)
char_mat(3,6)=( 2.d0,0.d0)
char_mat(3,7)=( 0.d0,0.d0)
char_mat(3,8)=(-1.d0,0.d0)
char_mat(3,9)=( 2.d0,0.d0)
char_mat(3,10)=( 0.d0,0.d0)
name_rap(4)="T_1g G_15' G_4+"
char_mat(4,1)=( 3.d0,0.d0)
char_mat(4,2)=( 0.d0,0.d0)
char_mat(4,3)=(-1.d0,0.d0)
char_mat(4,5)=(-1.d0,0.d0)
char_mat(4,6)=( 3.d0,0.d0)
char_mat(4,8)=( 0.d0,0.d0)
char_mat(4,9)=(-1.d0,0.d0)
char_mat(4,10)=(-1.d0,0.d0)
name_rap(5)="T_2g G_25' G_5+"
ir_ram(5)="R"
char_mat(5,1)=( 3.d0,0.d0)
char_mat(5,2)=( 0.d0,0.d0)
char_mat(5,4)=(-1.d0,0.d0)
char_mat(5,5)=(-1.d0,0.d0)
char_mat(5,6)=( 3.d0,0.d0)
char_mat(5,7)=(-1.d0,0.d0)
char_mat(5,8)=( 0.d0,0.d0)
char_mat(5,9)=(-1.d0,0.d0)
name_rap(6)="A_1u G_1' G_1-"
char_mat(6,6)=(-1.d0,0.d0)
char_mat(6,7)=(-1.d0,0.d0)
char_mat(6,8)=(-1.d0,0.d0)
char_mat(6,9)=(-1.d0,0.d0)
char_mat(6,10)=(-1.d0,0.d0)
name_rap(7)="A_2u G_2' G_2-"
char_mat(7,3)=(-1.d0,0.d0)
char_mat(7,4)=(-1.d0,0.d0)
char_mat(7,6)=(-1.d0,0.d0)
char_mat(7,8)=(-1.d0,0.d0)
char_mat(7,9)=(-1.d0,0.d0)
name_rap(8)="E_u G_12' G_3-"
char_mat(8,1)=( 2.d0,0.d0)
char_mat(8,2)=(-1.d0,0.d0)
char_mat(8,3)=( 0.d0,0.d0)
char_mat(8,4)=( 0.d0,0.d0)
char_mat(8,5)=( 2.d0,0.d0)
char_mat(8,6)=(-2.d0,0.d0)
char_mat(8,7)=( 0.d0,0.d0)
char_mat(8,9)=(-2.d0,0.d0)
char_mat(8,10)=( 0.d0,0.d0)
name_rap(9)="T_1u G_15 G_4-"
ir_ram(9)="I"
char_mat(9,1)=( 3.d0,0.d0)
char_mat(9,2)=( 0.d0,0.d0)
char_mat(9,3)=(-1.d0,0.d0)
char_mat(9,5)=(-1.d0,0.d0)
char_mat(9,6)=(-3.d0,0.d0)
char_mat(9,7)=(-1.d0,0.d0)
char_mat(9,8)=( 0.d0,0.d0)
name_rap(10)="T_2u G_25 G_5-"
char_mat(10,1)=( 3.d0,0.d0)
char_mat(10,2)=( 0.d0,0.d0)
char_mat(10,4)=(-1.d0,0.d0)
char_mat(10,5)=(-1.d0,0.d0)
char_mat(10,6)=(-3.d0,0.d0)
char_mat(10,8)=( 0.d0,0.d0)
char_mat(10,10)=(-1.d0,0.d0)
ELSE
CALL errore('set_irr_rap','code number not allowed',1)
END IF
RETURN
END
!--------------------------------------------------------------------------
FUNCTION is_complex(code)
!--------------------------------------------------------------------------
! This function receives a code of the group and provide .true. or
! .false. if the 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 " F 13 "C_3v" F 23 "D_6h" F
! 4 "C_2 " F 14 "C_4v" F 24 "D_2d" F
! 5 "C_3 " T 15 "C_6v" F 25 "D_3d" F
! 6 "C_4 " T 16 "C_2h" F 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 " F 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
LOGICAL :: complex_aux(32)
data complex_aux / .FALSE., .FALSE., .FALSE., .FALSE., .TRUE. , &
.TRUE. , .TRUE. , .FALSE., .FALSE., .FALSE., &
.FALSE., .FALSE., .FALSE., .FALSE., .FALSE., &
.FALSE., .TRUE. , .TRUE. , .TRUE. , .FALSE., &
.FALSE., .FALSE., .FALSE., .FALSE., .FALSE., &
.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= complex_aux(code)
RETURN
END FUNCTION is_complex
Reference in New Issue View Git Blame Copy Permalink