!-----------------------------------------------------------------------------------------!
! Copyright (c) 2018 Peter Grünberg Institut, Forschungszentrum Jülich, Germany !
! This file is part of Jülich KKR code and available as free software under the conditions!
! of the MIT license as expressed in the LICENSE.md file in more detail. !
!-----------------------------------------------------------------------------------------!
!------------------------------------------------------------------------------------
!> Summary: This subroutine defines the rotation matrices for all the 32 point groups
!> Author:
!> This subroutine defines the rotation matrices for all the 32 point groups and names them after
!> J.F. Cornwell (Group Theory??) second edition Appendix D, p 324-325
!------------------------------------------------------------------------------------
module mod_pointgrp
use :: mod_datatypes, only: dp
private :: dp
contains
!-------------------------------------------------------------------------------
!> Summary: This subroutine defines the rotation matrices for all the 32 point groups
!> Author:
!> Category: numerical-tools, KKRhost
!> Deprecated: False
!> This subroutine defines the rotation matrices for all the 32 point groups and names them after
!> J.F. Cornwell (Group Theory??) second edition Appendix D, p 324-325
!-------------------------------------------------------------------------------
subroutine pointgrp(rotmat, rotname, writesymfile)
implicit none
! optional input, can trigger writeout of symmetry matrices to sym.out file
logical, optional :: writesymfile
integer, parameter :: iou=3514 ! file unit for sym.out file
! .. Output variables
real (kind=dp), dimension(64, 3, 3), intent(out) :: rotmat !! Rotation matrices
character (len=10), dimension(64), intent(out) :: rotname !! Name of the space group
! .. Local variables
integer :: i, j, i1, is
real (kind=dp) :: rthree, half
rthree = sqrt(3.e0_dp)/2.e0_dp
half = 0.5e0_dp
! set to zero
do i1 = 1, 64
do i = 1, 3
do j = 1, 3
rotmat(i1, i, j) = 0.e0_dp
end do
end do
end do
rotmat(1, 1, 1) = 1.e0_dp
rotmat(1, 2, 2) = 1.e0_dp
rotmat(1, 3, 3) = 1.e0_dp
rotname(1) = 'E'
rotmat(2, 1, 2) = 1.e0_dp
rotmat(2, 2, 3) = -1.e0_dp
rotmat(2, 3, 1) = -1.e0_dp
rotname(2) = 'C3alfa'
rotmat(3, 1, 2) = -1.e0_dp
rotmat(3, 2, 3) = -1.e0_dp
rotmat(3, 3, 1) = 1.e0_dp
rotname(3) = 'C3beta '
rotmat(4, 1, 2) = -1.e0_dp
rotmat(4, 2, 3) = 1.e0_dp
rotmat(4, 3, 1) = -1.e0_dp
rotname(4) = 'C3gamma'
rotmat(5, 1, 2) = 1.e0_dp
rotmat(5, 2, 3) = 1.e0_dp
rotmat(5, 3, 1) = 1.e0_dp
rotname(5) = 'C3delta '
rotmat(6, 1, 3) = -1.e0_dp
rotmat(6, 2, 1) = 1.e0_dp
rotmat(6, 3, 2) = -1.e0_dp
rotname(6) = 'C3alfa-1'
rotmat(7, 1, 3) = 1.e0_dp
rotmat(7, 2, 1) = -1.e0_dp
rotmat(7, 3, 2) = -1.e0_dp
rotname(7) = 'C3beta-1 '
rotmat(8, 1, 3) = -1.e0_dp
rotmat(8, 2, 1) = -1.e0_dp
rotmat(8, 3, 2) = 1.e0_dp
rotname(8) = 'C3gamma-1'
rotmat(9, 1, 3) = 1.e0_dp
rotmat(9, 2, 1) = 1.e0_dp
rotmat(9, 3, 2) = 1.e0_dp
rotname(9) = 'C3delta-1'
rotmat(10, 1, 1) = 1.e0_dp
rotmat(10, 2, 2) = -1.e0_dp
rotmat(10, 3, 3) = -1.e0_dp
rotname(10) = 'C2x'
rotmat(11, 1, 1) = -1.e0_dp
rotmat(11, 2, 2) = 1.e0_dp
rotmat(11, 3, 3) = -1.e0_dp
rotname(11) = 'C2y'
rotmat(12, 1, 1) = -1.e0_dp
rotmat(12, 2, 2) = -1.e0_dp
rotmat(12, 3, 3) = 1.e0_dp
rotname(12) = 'C2z'
rotmat(13, 1, 1) = 1.e0_dp
rotmat(13, 2, 3) = 1.e0_dp
rotmat(13, 3, 2) = -1.e0_dp
rotname(13) = 'C4x'
rotmat(14, 1, 3) = -1.e0_dp
rotmat(14, 2, 2) = 1.e0_dp
rotmat(14, 3, 1) = 1.e0_dp
rotname(14) = 'C4y '
rotmat(15, 1, 2) = 1.e0_dp
rotmat(15, 2, 1) = -1.e0_dp
rotmat(15, 3, 3) = 1.e0_dp
rotname(15) = 'C4z'
rotmat(16, 1, 1) = 1.e0_dp
rotmat(16, 2, 3) = -1.e0_dp
rotmat(16, 3, 2) = 1.e0_dp
rotname(16) = 'C4x-1 '
rotmat(17, 1, 3) = 1.e0_dp
rotmat(17, 2, 2) = 1.e0_dp
rotmat(17, 3, 1) = -1.e0_dp
rotname(17) = 'C4y-1'
rotmat(18, 1, 2) = -1.e0_dp
rotmat(18, 2, 1) = 1.e0_dp
rotmat(18, 3, 3) = 1.e0_dp
rotname(18) = 'C4z-1'
rotmat(19, 1, 2) = 1.e0_dp
rotmat(19, 2, 1) = 1.e0_dp
rotmat(19, 3, 3) = -1.e0_dp
rotname(19) = 'C2a'
rotmat(20, 1, 2) = -1.e0_dp
rotmat(20, 2, 1) = -1.e0_dp
rotmat(20, 3, 3) = -1.e0_dp
rotname(20) = 'C2b'
rotmat(21, 1, 3) = 1.e0_dp
rotmat(21, 2, 2) = -1.e0_dp
rotmat(21, 3, 1) = 1.e0_dp
rotname(21) = 'C2c'
rotmat(22, 1, 3) = -1.e0_dp
rotmat(22, 2, 2) = -1.e0_dp
rotmat(22, 3, 1) = -1.e0_dp
rotname(22) = 'C2d'
rotmat(23, 1, 1) = -1.e0_dp
rotmat(23, 2, 3) = 1.e0_dp
rotmat(23, 3, 2) = 1.e0_dp
rotname(23) = 'C2e'
rotmat(24, 1, 1) = -1.e0_dp
rotmat(24, 2, 3) = -1.e0_dp
rotmat(24, 3, 2) = -1.e0_dp
rotname(24) = 'C2f'
do i1 = 1, 24
do i = 1, 3
do j = 1, 3
rotmat(i1+24, i, j) = -rotmat(i1, i, j)
end do
end do
rotname(i1+24) = 'I' // rotname(i1)
end do
! *********************************************
! Trigonal and hexagonal groups
! *********************************************
rotmat(49, 1, 1) = -half
rotmat(49, 1, 2) = rthree
rotmat(49, 2, 1) = -rthree
rotmat(49, 2, 2) = -half
rotmat(49, 3, 3) = 1.e0_dp
rotname(49) = 'C3z'
rotmat(50, 1, 1) = -half
rotmat(50, 1, 2) = -rthree
rotmat(50, 2, 1) = rthree
rotmat(50, 2, 2) = -half
rotmat(50, 3, 3) = 1.e0_dp
rotname(50) = 'C3z-1'
rotmat(51, 1, 1) = half
rotmat(51, 1, 2) = rthree
rotmat(51, 2, 1) = -rthree
rotmat(51, 2, 2) = half
rotmat(51, 3, 3) = 1.e0_dp
rotname(51) = 'C6z'
rotmat(52, 1, 1) = half
rotmat(52, 1, 2) = -rthree
rotmat(52, 2, 1) = rthree
rotmat(52, 2, 2) = half
rotmat(52, 3, 3) = 1.e0_dp
rotname(52) = 'C6z-1'
rotmat(53, 1, 1) = -half
rotmat(53, 1, 2) = rthree
rotmat(53, 2, 1) = rthree
rotmat(53, 2, 2) = half
rotmat(53, 3, 3) = -1.e0_dp
rotname(53) = 'C2A'
rotmat(54, 1, 1) = -half
rotmat(54, 1, 2) = -rthree
rotmat(54, 2, 1) = -rthree
rotmat(54, 2, 2) = half
rotmat(54, 3, 3) = -1.e0_dp
rotname(54) = 'C2B'
rotmat(55, 1, 1) = half
rotmat(55, 1, 2) = -rthree
rotmat(55, 2, 1) = -rthree
rotmat(55, 2, 2) = -half
rotmat(55, 3, 3) = -1.e0_dp
rotname(55) = 'C2C'
rotmat(56, 1, 1) = half
rotmat(56, 1, 2) = rthree
rotmat(56, 2, 1) = rthree
rotmat(56, 2, 2) = -half
rotmat(56, 3, 3) = -1.e0_dp
rotname(56) = 'C2D'
do is = 1, 8
do i = 1, 3
do j = 1, 3
rotmat(56+is, i, j) = -rotmat(48+is, i, j)
end do
end do
rotname(56+is) = 'I' // rotname(48+is)
end do
! for FS code we should be able to write out the symmetries to a file
if (present(writesymfile)) then
if(writesymfile)then
open(unit=iou,file='sym.out',form='formatted',action='write')
write(iou,'(I0)') 64
do is=1,64
write(iou,'(A)') ROTNAME(is)
write(iou,'(3ES25.16)') ROTMAT(is,:,:)
end do
close(iou)
writesymfile = .false.
end if ! writesymfile
end if ! present(writesymfile)
! ccccccccccccccccccccccccccccccccccccccccccccccccc
end subroutine pointgrp
end module mod_pointgrp
