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symmetry.f90
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symmetry.f90
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!
module symmetry
use accuracy
implicit none
public SymmetryInitialize,sym,correlate_to_Cs
type ScIIT
integer(ik) :: Noper ! Number of operations in the CII operator
integer(ik) :: Nzeta ! Number of symmetric elements taking into account the degeneracies
real(ark),pointer :: ioper(:) ! the operation number in the MS group
integer(ik),pointer :: coeff(:) ! coefficients of the CII operator
integer(ik),pointer :: izeta(:) ! symmetry indentification as a eigenvalues of the CII operator
end type ScIIT
type SymmetryT
character(len=cl) :: group = 'C' ! The symmetry group
integer(ik) :: NrepresCs = 2 ! Number of irreduc. represent. for Cs(M)
integer(ik) :: Nrepresen = 1 ! Number of irreduc. represent.
integer(ik) :: Noper = 1 ! Number of operations
integer(ik) :: Nclasses = 1 ! Number of classes
integer(ik),pointer :: Nelements(:) ! Number of elements in a class
integer(ik),pointer :: characters(:,:)! Character table
type(SrepresT),pointer :: irr(:,:) ! irreducible representaion
integer(ik),pointer :: degen(:) ! degeneracy
character(len=3),pointer :: label(:) ! The symmetry label
integer(ik) :: Maxdegen = 1 ! Maximal degeneracy order
integer(ik),pointer :: igenerator(:) ! address of the class generator in the sym%Ngroup list
type(ScIIT) :: CII ! the elements of the CII operator
real(ark),pointer :: euler(:,:) ! rotational angles equivalent to the group operations
end type SymmetryT
type SrepresT
real(ark),pointer :: repres(:,:) ! matrix representation of the group
end type SrepresT
type(SymmetryT) , save :: sym
contains
subroutine SymmetryInitialize(sym_group)
character(len=cl),intent(in) :: sym_group
integer(ik):: alloc,iclass,gamma,ioper,ielem
real(ark) :: o,p2,p3
!
sym%group=sym_group
!
select case(trim(sym_group))
case("C(M)","C")
sym%Nrepresen=1
sym%Noper=1
sym%Nclasses=1
sym%CII%Noper = 0
call simple_arrays_allocation
sym%characters(1,1)=1
sym%degen=(/1/)
sym%Nelements=(/1/)
sym%label=(/'A'/)
do gamma = 1,sym%Nrepresen
ioper = 0
do iclass = 1,sym%Nclasses
do ielem = 1,sym%Nelements(iclass)
!
ioper = ioper + 1
!
allocate(sym%irr(gamma,ioper)%repres(sym%degen(gamma),sym%degen(gamma)),stat=alloc)
!
if (sym%degen(gamma)==1) then
sym%irr(gamma,ioper)%repres(1,1)= sym%characters(gamma,iclass)
endif
!
enddo
enddo
enddo
case("CS(M)","CS")
sym%Nrepresen=2
sym%Noper=2
sym%Nclasses=2
sym%CII%Noper = 0
call simple_arrays_allocation
sym%characters= reshape( &
(/ 1, 1, &
1,-1 /),(/2,2/))
sym%degen=(/1,1/)
sym%Nelements=(/1,1/)
sym%label=(/'A''','A"'/)
call irr_allocation
case("C2V(M)","C2V")
sym%Nrepresen=4
sym%Noper=4
sym%Nclasses=4
sym%CII%Noper = 0
call simple_arrays_allocation
sym%characters= reshape( &
(/ 1, 1, 1, 1, & ! A1
1, 1,-1,-1, & ! A2
1,-1,-1, 1, & ! B1
1,-1, 1,-1 /),(/4,4/)) ! B2
sym%degen=(/1,1,1,1/)
sym%Nelements=(/1,1,1,1/)
sym%label=(/'A1','A2','B1','B2'/)
!
o = 0.0_ark
p2 = 0.5_ark*pi
p3 = 1.5_ark*pi
!
sym%euler( 1,:) = 0
sym%euler( 2,:) = (/pi,o,o /)
sym%euler( 3,:) = (/o,pi,o/)
sym%euler( 4,:) = (/p2,pi,p3/)
!
call irr_allocation
case("C2H(M)","C2H")
sym%Nrepresen=4
sym%Noper=4
sym%Nclasses=4
sym%CII%Noper = 0
call simple_arrays_allocation
sym%characters= reshape( &
(/ 1, 1, 1, 1, & ! Ag
1, 1,-1,-1, & ! Au
1,-1, 1,-1, & ! Bg
1,-1,-1, 1 /),(/4,4/)) ! Bu
sym%degen=(/1,1,1,1/)
sym%Nelements=(/1,1,1,1/)
sym%label=(/'Ag','Au','Bg','Bu'/)
!
call irr_allocation
case("G4(M)","G4")
sym%Nrepresen=4
sym%Noper=4
sym%Nclasses=4
sym%CII%Noper = 0
call simple_arrays_allocation
sym%characters= reshape( & ! E (12)(34) E* (12)(34)*
(/ 1, 1, 1, 1, & ! A+
1, 1,-1,-1, & ! A-
1,-1,-1, 1, & ! B+
1,-1, 1,-1 /),(/4,4/)) ! B-
sym%degen=(/1,1,1,1/)
sym%Nelements=(/1,1,1,1/)
sym%label=(/'A+','A-','B+','B-'/)
!
call irr_allocation
case("G4(EM)")
sym%Nrepresen=8
sym%Noper=8
sym%Nclasses=8
sym%CII%Noper = 0
call simple_arrays_allocation
sym%characters= reshape( & ! E a b ab E' E'a E'b E'ab
(/ 1, 1, 1, 1, 1, 1, 1, 1, & ! Ags
1, 1, -1, -1, 1, 1, -1, -1, & ! Aus
1, -1, -1, 1, 1, -1, -1, 1, & ! Bgs
1, -1, 1, -1, 1, -1, 1, -1, & ! Bus
1, 1, -1, -1, -1, -1, 1, 1, & ! Agd
1, 1, 1, 1, -1, -1, -1, -1, & ! Aud
1, -1, 1, -1, -1, 1, -1, 1, & ! Bgd
1, -1, -1, 1, -1, 1, 1, -1 /),(/8 ,8/)) ! Bud
sym%degen=(/1,1,1,1,1,1,1,1/)
sym%Nelements=(/1,1,1,1,1,1,1,1/)
sym%label=(/'Ags','Aus','Bgs','Bus','Agd','Aud','Bgd','Bud'/)
!
call irr_allocation
case default
write(out,"('symmetry: undefined symmetry group ',a)") trim(sym_group)
stop 'symmetry: undefined symmetry group '
end select
!
if (20<sym%Nrepresen) then
!
write(out,"('symmetry: number of elements in _select_gamma_ is too small: ',i8)") 20
stop 'symmetry: size of _select_gamma_ is too small'
!
endif
!
sym%maxdegen = maxval(sym%degen(:),dim=1)
!
! store the address of the group generator from ioper = 1..Noper list
!
ioper = 1
!
do iclass = 1,sym%Nclasses
!
sym%igenerator(iclass) = ioper
ioper = ioper + sym%Nelements(iclass)
!
enddo
contains
subroutine simple_arrays_allocation
integer(ik) :: alloc,nCII
nCII = max(1,sym%CII%Noper)
!
allocate (sym%characters(sym%Nclasses,sym%Nrepresen),sym%irr(sym%Nrepresen,sym%Noper),&
sym%degen(sym%Nrepresen),sym%Nelements(sym%Nclasses),sym%label(sym%Nrepresen),&
sym%igenerator(sym%Nclasses),&
sym%CII%ioper(nCII),sym%CII%coeff(nCII),sym%euler(sym%Noper,3),stat=alloc)
if (alloc/=0) stop 'simple_arrays_allocation - out of memory'
!
sym%CII%coeff = 0
sym%CII%ioper = 1
sym%euler = 0
!
end subroutine simple_arrays_allocation
subroutine irr_allocation
integer(ik) :: gamma,ioper,iclass,ielem,alloc
do gamma = 1,sym%Nrepresen
ioper = 0
do iclass = 1,sym%Nclasses
do ielem = 1,sym%Nelements(iclass)
!
ioper = ioper + 1
!
allocate(sym%irr(gamma,ioper)%repres(sym%degen(gamma),sym%degen(gamma)),stat=alloc)
!
if (sym%degen(gamma)==1) then
sym%irr(gamma,ioper)%repres(1,1)= sym%characters(gamma,iclass)
endif
!
enddo
enddo
enddo
if (alloc/=0) then
write (out,"(' symmetryInitialize ',i9,' error trying to allocate symmetry')") alloc
stop 'symmetryInitialize, symmetries - out of memory'
end if
end subroutine irr_allocation
end subroutine symmetryInitialize
function correlate_to_Cs(iparity,gu) result(isym)
!
implicit none
!
integer(ik),intent(in) :: iparity,gu
integer(ik) :: isym
!
if (sym%Nrepresen==sym%NrepresCs) then
!
isym = iparity
return
!
endif
!
if (iparity==1.and.gu==1) then
! A1
isym = 1
!
elseif (iparity==2.and.gu==1) then
! B1
isym = 3
!
elseif (iparity==1.and.gu==-1) then
! B2
isym = 4
!
else
! A2
isym = 2
!
endif
!
end function correlate_to_Cs
end module symmetry